Unit 3: Vibrations, Waves, Sounds, and Optics

Section 1: Waves

Lesson 0: Vibrations & Lesson1: The Natural of Waves & Lesson2,3: The Properties and Behavior of Waves


Class Notes
Simple Harmonic Motion(SHM)
  • Also called Simple harmonic oscillation(SHO)
  • ex) pendula(only when it has small initial angle).
Difference between Vibration and Oscillation
  • Vibration: broader term of repeating in motion
  • Oscillation: more narrow term that represents Regular and repeating vibration periodically.
Pendulum(approximate SHM)
  • T = 2pie * sqrt(length of string / gravity)
Energy of an Oscillation
  • EPE = (1/2) * k * x2
Waves
  • There are 2 types of waves: Mechanical and Electromagnetic.
  • Electromagnetic do not require medium.
  • Mechanical requires a medium.
  • Medium means material that carries the wave.
  • Medium is made of interacting particles.
Mechanical Waves
  • Longitudinal
    • The particles Oscillate parallel to the direction tthe wave travels
    • There is region of compression which has high pressure and parrticles are closer together
    • Also there is rarefaction region that has low pressurem and paarticles are farther
  • Transverse
    • The particles oscillate perpendicular to the direction the wave travels
    • Crest: max displacement
    • Trough: min displacement
    • Wave length: distance between on a point of a wave and the same point on the next wave
    • Amplitude(A): distance from equilibrium to crest or trough
    • Period: time for 1 complete cycle
    • Speed: v = d/t = (Wave Length) / (Period)
    • Frequency: how many waves pass in 1 second. f = 1 / T(period)
    • transvers_waves_001.jpg
Behavior of Waves
  • Reflection
    • When a wave encounters obsticle, bounces off of it.
    • Angle of inccidence = angle of reflection
    • Nature of boundary also determine the reflection
    • Boundary is where the medium changes
  • Refraction
    • Encounters a boundary, it changes direction when entering new medium, due to change in wave speed.
  • Diffraction
    • Encounters an obsticle or an openning and the wave bends a round and spreads out to fill in the space behind.
    • Bigger openning: less diffraction
    • shorther wave length: less diffraction
  • Interference
    • 2 waves traveling in the same medium, are at same place, at same time, their energy or amplitude is temporalily sum.

Summary
1. What is Vibration?
2. What is Wave?
3. What is frequency of Wave?
4. What is refraction?
5. What is Diffraction?
Vibration
  • When an object regular and repeat the "fashion"
  • back and forth
  • Caused by force
  • It stops due to dampling.(without dampling, it will continuosly vibrate
  • During the vibration, when an object is far away from the equilibrium point, restoring force will slow it down. ( restoring force makes an object to come back to its original position)
  • ex) bobble head doll, spring with mass, approximately pendulum
Periodic Motion
  • When an object regular and repeat the "motion"
  • Frequency means the number of cycles per period(Unit: Hz).
  • period means time that takes for 1 cycle.
  • period = 1 / frequency
  • frequency = 1 / period
  • Amplitude means the displacement of maximum position or minimum position from resting point
Pendulum Motion
  • When equilibrium position is the position when it is at rest, moving left side would be negative displacement and moving right would be positive displacement
  • There is always centripetal forces
  • There is Kinetic Energy and Gravitational potential energy in pendulum motion
  • I will not mention details for energies of pendulum because it is on the previous chapter and only repeating and reviewing
  • pendulum_energy.jpg
  • During pendulum motion, when an object is at its original position, it has the fastest velocity
  • The period of pendulum is time takes from one extreme(position that changes direction), pass the another extreme and come back to the starting extreme.
  • The period of pendulum is depend on length of string and gravity
  • The mathematical equation for pendulum is T = 2pie * sqrt(length of string / g)
Motion of a Mass on a Spring
  • Hooke's Law: mass on the spring and distance that strectched is directly proportinal
  • Kinetic energy and elastic potential energy exists.
  • Energy explanation is also in pervious notes and chapters and i didn't want to repeat.
  • The period of motion of a mass on a spring is simmilar to the period of pendulum motion however, in motion of a mass on a spring, spring constant and mass will affact therefore T = 2n * sqrt(mass / spring constatn)
  • mass_on_a_spring_energy.jpg
WAVES
  • Waves are everywhere in the nature
  • 2 most common waves are sound wave and light wave
  • Wave is a vibrating disturbance from a location to another location through median or empty spaces.
  • Motion creates disturbance
  • pulse is single disturbance
  • Medium is the material that carries the wave.
  • Medium is always made of particle to particle interaction
  • Waves transports energy phenomenon
Transverse wave vs Logitudinal wave vs Surface wave
  • In transverse wave, particles of medium move in perpendicular direction of the wave moves
  • In logitudinal wave, particles of medium move in paralell direction of the wave moves
    • ex) sound wave
  • In surface wave, particles of medium move in circular motion
    • ex) surface of Ocean


  • waves_categories.jpg

Electromagnetic wave vs Mechanical wave
  • Electromagnetic wave is able to move through vaccum, which means it doesn't need medium of particles to move through.
  • It is created when charged particles are vibrating
  • ex) Light wave
  • Mechanical wave is not able to move through vaccum. Therefore, it needs medium or interacting particles to move through
  • ex) Sound wave
Properties of Waves
  • Machenical waves
    • Crest
      • position when the medium is at maximum amount
    • Trough
      • Position when the medium is at minimum amount
    • Frequency
      • Unit: Hz(Hertz) -> 1 cycle / second
      • It refers when a wave moves through medium, how many times particles vibrated in specific period
      • f = 1 / T
    • Period
      • Symbol: T unit: (second)
      • The time that takes one complete cycle of a wave.
    • Wave Length
      • Symbol:external image lambda12.gif
      • Distance between crest to crest or trough to trough of one complete cycle
    • Amplitude
      • Displacement from equilibrium point to crest or trough
      • Square Directly related to amount of energy(Kinetic energy)
      • E = A ^ 2
    • Speed
      • Speed of disturbance of wave
      • speed = distance / time = wave length / period
      • Speed = wave length * frequency
  • Logitudinal
    • Compression region
      • when wave has maximum density and high pressure
    • Rarefaction region
      • When wave has minimum density and low pressure
    • Wave Length
      • Distance from same region to the next same region
Behavior of Wave
  • Boundary behavior.
    • When the medium is held by fixed end, the reflection occurs with inverse direction
    • When the medium is held by free end, the reflection occures in same direction.
    • When the pulse is transmitting from less dense medium to high dense medium, the pulse with same direction and slower speed (than reflected pulse) wave will transmitted to high dense medium and the pulse with inverse direction with slower(than original pulse) will reflected to less dense medium.
    • When the pulse is transmitting from high dense medium to less dense medium, the pulse with same direction and faster speed (than original) wave will transmitted to less dense medium and the pulse with same direction with slower(than transmitted pulse) will reflected to high dense medium.
  • Reflection
    • When the wave meets the barrier that cannnot go through or absorbed, wave is reflected to the different direction with same angle.
    • When the wave bounced by parabolic barrier, the wave will spread and reflected to different directions with same angle.
  • Refraction
    • When the wave pass from medium to another medium, and involves direction changes
    • Bends the path of wave
    • When medium changes, the speed will also changes.
    • For example, when wave from deep medium pass to shallow medium, the wave will slow down.
    • Angles become more perpendicular to the boundary
  • Diffraction
    • When the wave pass the openning through, the wave changes direction
    • The wave bends and tries to fill spaces behind the openning
    • When amount of diffraction increases, wave length also increases.
  • Interference
    • Occurs when the 2 waves meets when they are at same medium and same time.
    • 2types: Constructive and Destructive
    • Constructive is when both wave has same direction of amplitude and make an inccident
    • Destructive is when both wave has opposite direction of applitude and make an inccident
    • After interference, both waves just keep move like before
  • Doppler Effect
    • An effect that occurs due to the act of moving of the source of wave.
    • common example is moving sound wavebehavior_of_end.jpgBehavior_of_wave.jpg
Answer for Questions
1. What is Vibration?
  • Vibration is the act of motion that moves going back and forth, which means it repeats regular motion.
2. What is Wave?
  • Wave is vibrating disturbance that travels from place to place
3. What is frequency of Wave?
  • Frequency of wave is amount of the wave per specific time
4. What is refraction?
  • It happens when the wave go through an obsticle and change direction to closer to perpendicular
5. What is Diffraction?
  • Diffraction is one property of wave and it occurs when the wave pass through openning. When wave pass through the openning, it starts to spread out and tries to fill all spaces.


LAB: Mass on Spring
Object: What is the relationship between the force that a spring exerts on a mass and the distance the spring stretches?
Hypothesis: The distance of the spring's stretcheness is directly proportional to the mass that is on the spring because it will in crease weight which represents gravitational force that affects to the object.

DATA
springlabTable.jpgSpringlabGraph.jpg

Conclusion
The experiment proved that distance of the spring's stretcheness is directly proportional to the amount of the mass that is hanging on the spring. During the lab, we used the force when the spring is at rest and by adding mass, the spring stretched more and more. We also proved hooke's law which stated Spring force is equal to spring constant times change in distance. As you can see the equation on the graph, y = 97.76x and y = 3.0895x, in the equation y represents force of spring and the slope of the graph represents the spring force constance. In the lab, the possible sourece of error is the human error due to it was hard to make spring completely at rest and we only could measure approximate value of the distance.

Part B
Object: What is the relationship between the period of oscillation and the mass?
Hypothesis: When mass increases period will also increase because more mass means greater inertia. Also the relationship will be direct square root.
Data
partb_springlab_edited.jpg

Conclusion
The experiment proved the relationship between the period of oscillation and mass is directly square root proportional. By using formula T = 2pi * sqrt(m / k) we could determine what the slope and x represents. T = 2pi / sqrt(k) * sqrt(m) therefore slope represents 2pi / sqrt(k) and x represents mass. Also the coeffic What we got for slope is 3.09. However, theoretically, the slope should be 3.5. The possible source of error is that all humans have different counting speed, obsevation skills and reaction times. Therefore the result became different.


LAB: Slinky lab
Objective
To find therelationship between wave speed and frequency.
To find therelationship between wave speed and wavelength.
To distinguishbetween transverse and longitudinal waves.

Hypothesis: Frequency and wave speed are independent from each, and also the wavelength and wave speed are independent from each.

Data
Table 1 - Speed of pulses (Spring A)

5.0 meter total distance
10.0 meter total distance
Amplitude (cm)
10.0
20.0
30.0
10.0
20.0
30.0
Trial 1 time (s)
0.59
0.44
0.39
0.41
0.45
0.31
Trial 2 time (s)
0.6
0.53
0.35
0.31
0.43
0.35
Trial 3 time (s)
0.6
0.52
0.35
0.32
0.49
0.33
Avg.time (s)
0.6
0.5
0.36
0.35
0.46
0.33
Distance (m)
5.0
5.0
5.0
10.0
10.0
10.0
Avg. Speed (m/s)
8.3
10
13.8
28.6
22
30.3

Table 2 - Speed of pulses (Spring B)

5.0 meter total distance
10.0 meter total distance
Amplitude (cm)
20.0
30.0
40.0
20.0
30.0
40.0
Trial 1 time (s)
1.11
0.91
0.88
1.04
1
1.02
Trial 2 time (s)
1.127
0.89
0.87
1.03
0.95
1.01
Trial 3 time (s)
0.977
0.94
0.76
1.02
1
0.99
Avg.time (s)
1.07
0.913
0.8367
1.03
0.983
1
Distance (m)
5.0
5.0
5.0
10.0
10.0
10.0
Avg. Speed (m/s)
4.67
5.47
5.97
9.7
10.17
10

Discussion Questions
  1. How do the speeds of the waves compare for the 3 different amplitudes of the 5.0 meter distance?
  • It increased even it is not supposed to.
  1. Did amplitude influence the speed of the waves for the 5.0 meter distance?
    • Yes amplitude influenced the speed of the waves for the 5.0 meter distance in the lab; however, this is error and it should not increase
  2. How do the speeds of the waves compare for the 3 different amplitudes of the 10.0 meter distance?
    • It increased and decreased even it should not change
  3. Did amplitude influence the speed of the waves for the 10.0 meter distance?
    • Yes it did in this experiment; however this is error and it should not change
  4. How do the speeds of the waves compare for the 5.0 meter and 10.0 meter distances?
    • Speed of the wave for 10.0 meter distance is faster than speeds of the wave for the 5.0 meter.
  5. What changed when you measured the time for 10-m vs. the 5.0-m distance? Choose as many as apply.
    1. The medium changed.(o)
    2. The wavelength changed.(o)
    3. The speed changed.(o)
    4. The frequency changed.(x)

  1. How do the speeds of the waves compare for the 2 different types of springs?
    • Spring A had faster speed.
  2. What are some differences between the longitudinal and the transverse wave?
    • Longitudinal wave has compression region and rarefaction region and changes its pressure. Also its moves parallel to ground. Transverse wave do not have compressed region and rarefaction region and moves perpendicular to the ground.


Interesting applet about what medium change effect to the wave
medium_changes_velocity.JPG
http://faraday.physics.utoronto.ca/PVB/Harrison/Flash/Waves/TwoMediums/TwoMediums.html
The applet shows that when you change medium, the speed of wave also changed.

Section 2 : Sound waves and Music

Lesson 4: Standing Waves & Lesson 1: The Nature of Sound Wave & Lesson 2: Sound Properties and Their Perception & Lesson 3: Behavior of Sound Wave


Class Notes
Resonance
  • When the natural frequency of an object is reinforced by an external object
  • Causing a standing wave to form
Standing Waves
  • A pattern created by the interference of a wave due to resonance
n represents number of antinodes
Antinodes
  • Position of maximum amplitude
Nodes
  • Position where string is not moving because of interference of constructive wave and destructive wave.
Equations
  • fn = fi * n
  • L = (1/2) * wave length * n
  • v = f * wave length
  • f = (nv) / 2L --> this equation is short cut of combination of 2nd and 3rd dots
  • v = sqrt(T / linear density)
Doppler Effect Equation
  • perceived frequency = actual frequency * ((speed of sound in air + - speed of observer) / (speed of sound in air - + speed of souurce of sound))
  • When if distance between source and observer decreases, use + - ( toward)
  • When if distance between source and observer increases, use - +(away)

Summary
1. What is traveling waves?
2. What is Standing waves?
3. What is Doppler effect?
4. What is difference of sound wave compare to other waves such as water wave?
5. What is nodes?

Standing waves vs Traveling waves
  • Traveling waves
    • Waves that moves through the medium and it is found in non-fixed space of medium
    • Have regular wave pattern
  • Standing waves
    • The wave pattern that is observed in fixed point and medium is standing still.
    • It causes by interference of wave and reflected wave
    • Nodes and aniti nodes are main characteristic of standing waves
    • Nodes: points of medium that never moves
    • nodes have minimum displacement
    • Anti-nodes have maximum displacement
    • When a standing wave pattern is created at specific frequency, and canceled out, the frequency is called harmonics
    • harmonics are refered as the number of anti- nodes
    • each loop is equal to half of wave length therefore Length = n * (1/2) * wave length
    • Harmonics_sample.jpg
Sound Wave
  • Sound wave is one common wave that we can easily experience
  • It is mechanical logitudinal wave that transports energy through any medium such as air
  • Therefore air particles creates compression and rarefraction, which means the sound wave involves pressure.
  • In compression region, air have high pressure and at rarefaction region, the air have low pressure
  • Pressure_of_sound_wave.jpg
Properties of Sound Wave
  • Sound wave has some same properties of common wave has
  • Therefore there is period, frequency and speed exists
  • Human ear can recognize 20 ~ 20000Hz of sound wave
  • Infrasound is any sound that have lower frequency than 20 Hz
  • Ultrasound is any sound that have higher frequency than 20000Hz
  • In musical theory, they detects the change of frequencies. For example, octave means the sounds have frequency ratio of 2:1 such is 1000Hz and 500 Hz
  • Intensity represents transported energy through the given area; threrefore, the mathematical formula is Intensity = Power / Area
  • Intensity approximately described as loudness of the sound so it is square inversly related with distance
  • Intensity is measured with decibel scale and 0dB represents threshold of hearing(sounds that humans can comfortabely detect without any damage).
  • Pitch represents the when you feels like sound is increasing even though the intensity didn't increase
  • dB_scale_sample.jpg
  • Speed of sound wave is different when the medium changes.
  • Usually solid has highest speed of sound wave, and gas has lowest speed of sound wave
  • This represents the elastic properties
  • When the medium has more dense, due to it has more inertia, the sound wave will slow down
  • This represents the inertial property
  • v = distance / time
  • v = wavelenght * frequency
Human ear
  • It is the human body's system that can detect the pressure change of sound wave
  • There are 3 major parts: outer ear, inner ear and middle ear
  • Outer ear collects the sound and send to middle ear. Middle ear changes forms of energy of sound wave that inner ear can detect. Inner ear detects the sound and sent information to nerve system.
  • What inner ear detects is the vibration of eardrum that produced by compression of sound wave
  • human_ear.jpg
Behavior of Sound Wave
  • Both constructive interference and destructive interference exists in sound wave
  • The explanation for both term is on previous lesson
  • Constructive interference will occur anti - nodes and destructive interference will occur nodes
  • By using destructive interference, noise is able to cancel out or reduced.
  • The difference between music and noise is that music has clear mathematical equation and relationship between sound wave while noise does not have
  • Beat frequency is frequency difference between 2 sound waves.
  • Beats occurs between the similar frequency of sound wave
  • The graph is shown when the two sound wave were added
  • beat_pattern.jpg
  • With fixed end boundary, pulse will reflected
  • When the medium is connected with different medium and tries to transfer the pulse, you will have less reflection and more transmission when you connect simmilar dense of mediums.
  • sound_wave_boundary_behavior.jpg
  • Reflection of sound wave has two types: echo and reverberation.
    • Reverberation only occurs in 17 meter height, width , length dimension room because human brain only has 0.1 second of sound memory
    • Echo happens when the sound reach the ear after 0.1 second.
    • Parabolic shape can collect more sound waves
    • Also the smoothness of the wall will affect the feeling of sound wave
    • soundwave_wall_difference.jpg
  • The sound wave also have behavior of diffraction and it is simmilar to the diffraction of other waves such as water wave
    • wave length = speed / frequency
    • ex) bat
  • Refraction of sound wave changes speed of the sound wave
    • ex) when the sound wave travels over the water
Doppler Effect and shock waves
  • Doppler effect of sound wave occurs due to the moving of source of sound
  • When source of doppler effect is moving closer to the obsever, the pitch increase
  • Observer will feel wavelength decrease and frequency increase when the source of wave moves toward observer
  • When the source of wave is moving at same speed of sound, it will produce shock wave because the waves that is in front of the source will put on the same places.
  • Sonic boom will created when the source of sound moves faster than the speed of the sound. It has high compression and you will hear sound later you see the source.
  • sonicboom_and_shock_wave.JPG

Answers
1. What is traveling waves?
  • Traveling wave is the wave that travels through the medium.
2. What is Standing waves?
  • Standing wave is the wave that moves through the medium that is standing still.
3. What is Doppler effect?
  • It occurs when the source of sound is moving. To observer, frequency and wavelenght feels like changing
4. What is difference of sound wave compare to other waves such as water wave?
  • Sound wave can move through vairety types of medium and has echos when it is reflecting
5. What is nodes?
  • node is the position when the medium is not moving and has least position due to destructive interference and canceled out.

Lab: Transverse Standing Waves on a String

Object: To determine the relationship between the number of harmonics, the frequency of the source, and the wavelength of transverse waves traveling in a stretched string.

Hypothesis: Frequency and number of harmonics would directly proportional. In addition frequency and the wavelenth would have inverse relationship, frequency and tension would have square direct relationship.

Data

Table_for_standing_waves.jpg
Standing_wave_Chart_1_edit.JPG
Standing_wave_Chart_2.jpg
Standing_wave_Chart_3.jpg

1. What is the name given to a point on a vibrating string at which the displacement is always zero?

  • Nodes are points on a vibrating string at which the displacement is always zero.

2. What is the name given to a point at which the displacement is always a maximum?

  • The point at which the displacement is always a maximum is called anti-nodes.
3.How is the length of the string related to the wavelength for standing waves?

  • When number of anti nodes increase in standing wave, wavelength always decrease because it is only the length of 1 complete cycle, which means length of 2 anti nodes.

4.What is the longest possible wavelength for a standing wave in terms of the string length?

  • The longest possible wavelength for a standing wave is double of string length

5. Use your graph to find the frequency for n = 20. (Try it. Does it work?)
  • 20 * 11.805 is equal to frequency for n = 20. Therefore frequency is 236.1 Hz.

6. What is the relationship between the speed of the wave and the harmonic number?

  • There is no relationship between the speed of the wave and harmonic number.

7. What is the relationship between the speed of the wave and the frequency?

  • Speed of the wave and frequency have no relationship. Speed won't change because even though frequency increases, wavelength will decrease.
8. What is the relationship between the wavelength and the harmonic number?

  • Wavelength and the harmonic number have inverse relationship because when harmonic number increases, frequency will also increase and therefore wavelength will decrease.

9.What is the relationship between the wavelength and the frequency?
  • The wavelength and the frequency have inverse relationship because when the wavelength increase, frequency increases.
Calculation
  • Calculate the speed of the wave for each harmonic. (SHOW A SAMPLE CALC!)
    • v = f * wavelength. therefore v = 11.7 * 14.38 = 168.246m/s
  • Calculate the tension in the string. (SHOW A SAMPLE CALC!)
    • F = m * g . F = 0.5 * 9.8 = 4.9N

Analysis
  • In the lab, we proved that frequency and number of harmonics are directly proportional, frequency and the wavelenth have inverse relationship and, frequency and tension have square direct relationship. In addition, we proved that the slope of the first data chart, 11.805, is the fundamental frequency. By using f = v / 2L, we could determine the velocity of wave in string, which was 169.76 m/s. The velocity value should be constant in the data table 1 because the v = sqrt( tention / linear density), and the tension of the medium in the experiement didn't change at all. Also in data chart 2, which proved the inverse relationship of frequency and wavelength, provided the simmilar velocity as data chart 1. Due to f = y = v / wavelength, v is equal to the A value in y = Ax ^ -1, which was 170. 59. It was simmilar to the velocity value i calculated in data chart 1. In data chart 3, which proved that frequency and tension are square directly related, showed the formula of fn = n / (2L * sqrt( linear density)) * sqrt(T) and B in the y = B * sqrt(x) is equal to n / (2L * sqrt( linear density)) and the value was 15.756. The source of error is human error because we are not able to perfectly notice the harmonics frequency and also the machine had limit of quantity.

Interesting applet about Doppler Effect
doppler.jpg
http://www.upscale.utoronto.ca/PVB/Harrison/Flash/ClassMechanics/DopplerWaveFronts/DopplerWaveFronts.html
this applet about doppler effect will help you to understand what doppler effect is and also you can change the speed of source and actually see the how wave moves.


Lesson 4: Resonance and Standing Wave & Lesson 5: Musical Instrument


Class Notes
Intensity
  • related to the rate of energy used to create sound and the distance from the source
  • I = Power / Area
  • P = Work / time
  • Area = surface area = 4πr2
  • Units: Watts / m2
  • Also measured by dB(decibels)
  • dB also called sound level or intensity level
  • dB = 10 log(I / Io)
  • Io = 1 x 10-12

Intensity
Intensity level(dB)
Threshold of pain
10
180
Threshold of discomfort
1
120
Talking
1 x 10-6
65
Whispering
1 x 10 -10
20
Threshold of hearing
1 x 10-12
0
  • Range Human hearing 20 ~20000 Hz
  • Range of Human Voice 85 – 1100 Hz
  • vair = 331.5 + 0.6T
  • T represent temperature
Property of sound
  • Reflection
    • Echo : larger distance, v = d / t
    • Reverberation: only small distance(less than 17meter)
    • Refraction
      • Change of speed due to change of medium and it seems like changing direction
      • Ex) during fall time, air near ground is warm and air above the ground is cooler therefore the sound will bent to upward and direct to cooler air
      • Diffraction
        • Same as before. It occurs when a sound wave pass an opening through
        • Interference
          • Resonance in strumpet tubes
            • When the sound wave, vibration of the air particle, hit the other object that can vibrate, it forces the object vibrate also
  • Beats:
    • interference of two sounds that are almost identical
    • Number of beats per second is equal to the difference between two frequencies
    • # beats = abs( f1 – f2)
  • When 2 speakers in a row are played at same time, there would be the region that there isn’t any sound existing due to destructive interference.

Summary
Questions
  1. What is resonance?
  2. What is fundamental frequency?
  3. What is difference between open end air column and closed end air column?
  4. What is number of harmonic number represent?
  5. What is natural frequency?


Natural Frequency
  • Objects are tends to vibrate in variety of situations such as hitting.
  • The vibrating object will also produce the sound wave
  • All objects have natural frequency that wants to vibrate
  • For example, each guitar strings have different sounds
Forced Vibration
  • When an object vibrate, the other objects that is connected to it will also starts to vibrate
  • For example, tuning fork on the openned box has louder sound because box also vibrates
  • When an objects force to vibrate the othe similar object, and due to constructive interference, the amplitude and feeling of loudness will increase.
  • When an object is forced vibrate, it have same frequency with the object that forced it to vibrate
Fundamental frequency
  • Fundamental frequency is the frequency that results 1 harmonic(at first harmonic)
  • Fundamental frequency also known as harmonic frequency
  • Harmonics represents the number of antinodes and the standing wave can specified by the harmonics
  • nodal point in standing wave represents position of node
  • antinodal point in standing wave represents position of antinode
  • All about standing wave are same as I explained before in the other summary
  • To find the frequency, use f = v / wavelength formula
  • To find the specific harmonic frequency, just multiply the harmonic number and fundamental frequency
  • Length of string is equal to product of (1/2) , wavelength and harmonic number
  • String_stand_wave_pattern_diagram.jpg
Resonance
  • Resonance means when the vibrating object force vibrate the other object that has same natural frequency.
  • Resonance explaines how musical instruments can make impressive sounds.
  • There are lot of examples of resonance in our common life.
  • Ex) We can hear sound of sea in sea shell.
  • Ex2)When we make guitar string vibrate, the guitar's body also vibrates and amplify the sound of harmonic frequency of guitar string.
  • Resonance_diagram.jpg
Open end air columns vs Closed end air columns
  • Open end air columns
    • When a tube, which sound wave move through and results standing wave pattern, has opennings at both ends.
    • It also has same equation to solve the length of tube or wavelength
      • L = (1/2) * wavelenght * n
    • However, it's diagram of standing wave pattern is unique and different compare to closed end air columns or string.
    • open_end_air_column_diagram.jpg
  • Closed end air columns
    • When a tube, which sound wave move through and results standing wave pattern, has covered end at one of the ends.
    • It has different equation to solve the length of tube or wavelength
      • L = (1/4) * wavelenght * n
      • In this case n alwas be odd number
    • The reason it only have odd number of harmonic number is that when closed end air columns had even number, its only openning would have nodal point which has minimum amplitude and have no sound.
    • closed_end_air_column_diagram.jpg


Answers
  1. What is resonance?
    • Resonance is when the vibrating object force vibrate the other object that has similar natural frequency
  2. What is fundamental frequency?
    • Fundamental frequency means the frequency of the first harmonic in standing wave pattern
  3. What is difference between open end air column and closed end air column?
    • Open end has opennings at both end but closed end has 1 openning at one side of end
  4. What is number of harmonic number represent?
    • Harmonic number represents the number of antinodes
  5. What is natural frequency?
    • Natural frequency is the frequency that objects wants to vibrate and object sometimes have same natural frequency.

LAB: Resonance Tube
Objective: What is the relationship between the length of a tube and its resonant frequencies?
Hypothesis: The length of a tube and its resonant frequencies will have direct relationship.

Data
Table_resonance_tube_lab_edited.jpg
resonance_lab_chart.jpg
data a is closed tube and data b is open tube

Calculation
  1. Calculate the speed of sound
    • v = 331.5 + 0.6T, T = 27.5 v = 331.5 + 0.6(27.5) = 348
  2. Using your data in parts A and B, calculate the percent Error between the experimental lengths and theoretical lengths
    • % error = (Abs(theoretical - experimental) / theoretical) * 100. % error = (Abs(0.13375 - 0.067) / 0.13375) * 100 = 49.91 %

Questions
  1. For an ideal resonance tube, an antinode occurs at the open end of the tube. What characteristic of real resonance tubes slightly alters the position of this antinode?
    • Diameter of the tube and chaos of air will alter the position of this antinode.
  2. Why must there be an antinode at the end of the resonance tubes?
    • Because if there is only nodes at the end of the resonance tube, we would not hear anything because sound cancels out by destructive interference in nodes.
  3. How long would the closed tube have to be to get the 10th harmonic?
    • 0.1253x = L therefore lenght of the closed tube to get the 10th harmonic is 0.1253 * 10 = 1.253m
  4. How long would the open tube have to be to get the 10th harmonic?
    • 0.253x = L therefore lenght of the closed tube to get the 10th harmonic is 0.253x * 10 = 2.53m
  5. Draw a figure showing the fifth resonance in a tube closed at one end. Show also how the length of the tube L5,is related to the wavelength, λ.
    • ()()( L5 is 5 * (1/4) * wavelength
  6. Draw a figure showing the fifth resonance in an open tube. Show also how the length of the tube L5,is related to the wavelength, λ.
    • )()()()()( L5 is 5 * (1/2) * wavelength.

Analysis
  • In the lab, we proved that the length of a tube and its resonant frequencies are directly related. When we see the graph and analysis, we used L = (1/2)wavelenght* n for the open ended tube which is data B. The equation was y = 0.253x where y represents the length of the tube and x represents the harmonic number, the slope, 0.253, is equal to (1/2)wavelength. By using wavelength = v / f, we determined v = slope * 2f and got 328.9 m/s velocity it had slight difference compare to the theoretical velocity value that we calculated in calculation1. Similarly, we used L = (1/4) * wavelenght * n for the closed ended tube which is data A. The equation was y = 0.1253x where y represents the length of the tube and x represents the harmonic number, the slope, 0.1253, is equal to (1/4)wavelength. By using wavelength = v / f, we determined v = slope * 4 f and got 325.78 which also had slight difference with theoretical value of velocity of air. The source of error is that the diameter of tube was changed while we were taking the small tube out of the big tube and also unlike ideal air, there is chaos in real air. Therefore the error must occur. To reduce the error, we had to subtract the 0.08 for theoretical length of opened tube and subtract the 0.04 for theoretical length of closed tube.


Interesting animations about beats
beats_tester.jpg
http://faraday.physics.utoronto.ca/PVB/Harrison/Flash/ClassMechanics/Beats/Beats.html
You can hear both sound that has slight different in frequency and hear the beats they make to compare with them.



Section 3: Light Waves and Color & Section 4: Reflection and Ray Model of Light

Lesson 1: How Do We Know Light is a Wave? & Lesson 3: Mathematics of Two Point Source Interference & Lesson 1: Reflection and its Importance & Lesson 2: Image Formation in Plane Mirror



Class Notes

Electromagnetic wave
  • Can travel through vacuum
  • Source is accelerating charged particle
  • Speed of light = c = 3 x 10^8 m/s in a vacuum
  • Linear propagation: tends to travel in straight line
  • 10^4 Hz – 10^24 Hz
Small wavelength, high frequency, high energy
Gamma ray
^
X rays
|
Ultra violet
|
Visible
|
Infrared
|
Microwave
Big wavelength, low frequency, low energy
Radio

Optical density
  • More optically dense, slower light travels
  • The value is decided by how can the material make the light slow
  • Transparent material allows light travel through without much energy loss or direction changes. : fully transmission
  • Opaque no transmission happens
  • Translucent material only allows partial transmission of light (some are absorbed some are reflected, some travels through) and change little direction of light.
Particle vs Wave
  • In 1800s, people thought the light is particle.
    • Corpuscular
    • “optics”
    • However, Young proved that the light is wave because his experiment showed diffraction of wave of light that cannot be explained by particle theory.
    • BUT Einstein proved that light is also particle by experimenting photoelectric effect.
    • Each of the result of experiments are not able to explained with both particle theory and wave theory

Young’s experiment
  • Diffraction
    • Light bends around an obstacle or through an opening create an interference pattern (due haygen’s principle)
    • Wavelength must be on the same order of magnitude as the opening or obstacle (about 10-7)
    • Less diffraction as opening decreases in size pattern will be closer together
    • Central antinode is very bright(2x), double width fringe is the pattern to the right and left of central antinode

  • Interference in 2 slits looks similar to diffraction
    • Central antinode is same width and same brightness as fringe
    • Distance between slits increases get closer pattern
    • Diffraction grating has hundreds or thousands of slits per mm
    • As wavelength decrease, pattern gets closer

Image characteristics
  • Type:
    • Real: light is actually at the position it seems to be, Can be projected
    • Virtual: light is Not really where it seems to be(illusion)
      • Ex) mirror
  • Orientation
    • Upright
    • Inverted
  • Size
    • Enlarged
    • Uncharged
    • Reduced
  • Location
    • Relative to the optical plane and/or the focal point
  • Law of reflection
    • Angle of incidence = angle of reflection

Questions
  1. How can you prove the light is a wave?
  2. What is polarization?
  3. What is Law of Reflection?
  4. What is the role of light to sight?
  5. Why is an image formed?


Light Wave
  • Light is electromagnetic wave
  • Light has both characteristics of particle and wave
  • Light can reflect, refract, diffract, and result doppler effect like other waves do
  • Reflection of light causes the forming of image
  • Incident angle is equal to bounced angle
  • Refraction occurs when the light moves from one medium to the other medium.
  • When a light pass through the bouundary, it bents
  • Diffraction happense when a light pass an opening through or change the medium and due to the change, the dircetion of light also changes and spread out
  • Light wave also have behavior to result both destructive interference and constructive interference.
  • Young discovered the light also produce two point source pattern like other waves do.
  • For the another reason to prove that light is a wave is that when the light hit the thin film, some light reflected back and some light refracted into the film and then reflected back later.Both reflected waves have same angles and distance
  • Unpolarized light means the light wave that has more than 1 vibrating plane
  • The process of changing the unpolarized light to polarized light is called polarization
  • There are 4 ways to occure polarization
    • By Transmission
      • Involves polaroid filter to eliminate one plane of the unpolarized light
      • Polaroid filter will choose the axis that is going to be filtered
    • By Reflection
      • Only when the unpolarized light bounces off on the non metallic material
      • Parallel to surface
    • By Refraction
      • Perpendicular to surface
    • By Scattering
      • When the light hit the atom of material and the electrons of atoms starts to vibrated and create its own electromagnetic wave
      • New wave and old wave will strike each.
      • polarization.jpg
  • In the two point source interference, Antinodal lines and nodal lines are exist.
  • They have order number counted from central antinodal lines,0, and increase by whole number therefore 1st antinodal line has 1 order number.
  • The order number of nodal lines are 0.5 if it is between central antinodal line and 1st antinodal line and increase by whole number.
  • nodal_antinodal_lines.jpg
  • Path difference is the difference in distance to travel to the same location from source 1 and source 2 of two point source interference.
  • The equation is ABS(distance from s1 - distance from s2)
  • If the location is on the nodal line or antinodal line, you can also use PD = order numer * wavelength
  • young's equation: wavelength = (y * d) / (m *L)
  • Where y is equal to distance , moon,to location perpendicularly from central anti nodal line, d represents the distance between source 1 and source 2, m represents order number, and L represents the length of central antinodal line
  • In the young's experiment, d represents the slit seperation distance, L represents the length between slit and screen, y is given and related to m(order number)
  • Coherent means the relationship of two light sources that have constant phase differencee
  • The lights must coherent to result the interference


Reflection
  • Luminous objects represent the objects that can make a light from itself.
    • ex)sun
  • Illuminous objecs represent the objects that are not able to make a light itself, but able to reflect the light
    • ex) human, moon... etc
  • Without light, we cannot see anything, which means there is no sight
  • We can see illuminous objects when they reflect lights to our eyes
  • Line of sight means the direction of sight to see what you want to see
  • Incident ray: light that hit the object
  • Reflected ray: light that is bounced off from the object
  • Distance from mirror to object is equal to the distance of the object's image
  • The law of reflection stated that the angle between nomal line, the line that is perpendicular to the surface of an object start from the point where incident ray hit, incident ray,angle of incident, is equal to the angle between normal line and reflected ray, angle of reflection.
  • law_of_reflection.jpg
  • We can specify reflection by the surface of an object that light is reflecting.
    • Specular reflection occurs when the surface of an object is smooth such as water and mirror.
    • All incident ray will be parallel to each and all reflected ray will be parallel to each
    • Diffuse reflection occurs when the surface of an object is rough such as mountain and ground.
    • The law of reflection still exist.
    • surface_difference_of_reflection.jpg
  • Image is not a real object but illusion that is reflected in mirror.
  • Image is formed due to the reflection of lights that travel into your eye
  • Image is located at same distance of object away from the mirror
  • Virtual image is an image that is formed in the location that light didn't reach
  • image_form.jpg
  • Real image is the image that is formed in the location where light can reach
  • Image by plane mirror is reversed left and right and upright
  • Image formed by plane mirror has 1:1 ratio in size with original object
  • Ray diagram shows that the person's view of image
  • Ray_diagram.jpg
  • Although you are farther or closer from the plane mirror, the portion of mirror you need to view image never change.
  • mirror_portion_of_vie.jpg
  • With two plane mirror you can make right angle mirror
  • In right angle mirror, you can see 3 images.
  • Image on the left side and right side are called primary image and they have same view of image with single plane mirror
  • The image on the middle side is called secondary image and it does not reverse left and right side
  • The reason the image on the middle side do not reverse left right side is that it reflects twice
  • right_angle_mirror.jpg
  • Usually when the angle of two plane mirror decrease, the number of image increase.
  • At 0 degree, which represents parallel mirrors, have infinate image.

ANSWERS
  1. How can you prove the light is a wave?
    • Light has many behavior of wave such as reflection, refraction and diffraction that cannot explained if light is particle
  2. What is polarization?
    • Polarization is the process that change unpolaried light wave to polaried wave by using polaroid filter
  3. What is Law of Reflection?
    • Law of reflection stated that reflected angle is equal to incident angle
  4. What is the role of light to sight?
    • If there is no light, then there is no sight
  5. Why is an image formed?
    • Image is formed when an light of object is reflected to another object such as mirror, to our eye.

LAB: Reflection of Plane Mirror
Objective: Demonstrate that reflection from a plane surce the angle of incidence is equal to the angle of reflection.

Data

Ray
Angle of Incidence, q1
Angle of Reflection, q2
Difference in Angle
Percent Error
1
30
29
1
3.44827586
2
48
45
3
6.66666667
3
60
60
0
0
4
14
12
2
16.6666667
5
70
70
0
0
0721010017.jpg

Data_chart_for_reflection_of_plane_mirror_lab.jpg

  1. Are your data consistent with the law of reflection? State your answer as quantitatively as possible.

  • Some of them are consistent with the law of reflection. For example, Ray number 5 has 70 degree of angle of incidence and 70 degree of angle of reflection. The angle of incidence and angle of reflection are equal therefore the ldata was consistent with the law of reflection. However, some of them were not equal which means error but it is not big error only slight difference.2. Where is the image in a plane mirror located?

  • Image in a plane mirror is located at the same distance as object from the mirror.



3. If you were required to graph the angle of incidence vs. the angle of reflection, what would be the shape of the graph? What would the slope of the line be?

  • The shape of the graph would be the linear graph that starts from 0. The slope would be 1 therefore the equation would be y = x.



4. What are the characteristics of all images from plane mirrors?
  • The left side and right side are reversed and it has the same distance as the objects distance from the mirror.
Interesting Applet for refraction and reflection
reflection_and_refraction.jpg
http://www.upscale.utoronto.ca/PVB/Harrison/Flash/Optics/Refraction/Refraction.html
This applet helps people to understand relations between refraction angle and index of refraction.

Section 3: Refraction and Ray Model of Light

Lesson3:Concave Mirror & Lesson4: Convex Mirror & Lesson 1:Refraction at boundary & Lesson 2: The mathematics of Refraction

Summary
Question
1. What is concave Mirror?
2. What is convex Mirror?
3. What is the relationship of incidence angle and refraction angle
4. What is snell's Law?
5. What is index of refraction?
Spherical Mirror
  • Also called curved mirror
  • Principle axis represents the line that pass through the center of the mirror. Lights toward the mirror is parallel to the principle axis
  • Vertex represent that point where light and mirror meet
  • Focal point represent the middle point between center of curvature and vertex. The reflected light is focused on the focal point.
  • Center of curvature is center of the original sphere that the mirror was part of it
  • Radius of curvature is the radius of the original shpere that the mirror was part of it. It has twice longer length than focal length
  • Focal length is length between vertex and focal point.
  • Aberration of spherical mirror results image blurry.
  • Anatomy_of_spherical_mirror.JPG
  • There are two mathematical equations for the spherical mirror
    • (1/f) = (1/object distance from mirror) + (1/ image distance from mirror)
    • (height of image / height of object) = -(image distance from mirror / object distance from mirror)
    • When focal point has positive value, there is concave mirror in situation. When it has negative value, there is convex mirror in situation.
    • When the distance of image is at positive location, the image is real image and when the distance of image is at negative location, the image is virtual image.
    • When the height of image is positive value, the image is uprighted and when the height of image is negative value, the image is inverted.
  • Concave Mirror
    • Mirror that has silver on the insided of the sphere.
    • Can create both vitual image and real image
    • When an object is behind the center of curvature, the real image that is inverted upside down will formed in the position between center of curvature and focal point. The image will have reduced size than an object.
    • When an object is between the center of curvature and focal point, the real image that is inverted will formed in the postion behind of the center of curvature. The image will have larger size than an object.
    • When an object is between the focal point and vertex, the virtual image that is uprigthed will formed. The image will have larger size than an object.
    • When an object is at focal point, no image will formed
    • When an object is at center of curvature, the real image that is inverted will formed at center of curvature. Image will have same size as an object.
    • concave_mirror.JPG
    • When the rays that are parallel to the principle axis are reflected by concave mirror, the reflected rays will pass the focal point.
    • When the rays that pass the focal point are reflected by concave mirror, the reflected rays will be parallel to the principle axis
    • Ray diagram shows the location where an image will created.
    • This is the process of drawing ray diagram
    • Process_of_ray_diagram.JPG
    • When the object is between focal point and vertex, you just have to extend the lines you draw to the back of the mirror.
  • Convex Mirror
    • Mirror that has silver on the outside of the shpere
    • Only can form vitual image that has reduced size and uprighted. Due to it is virtual image, it seems like formed behind the mirror
    • Focal point and center of curvature are on the behind the mirror
    • The process to draw a ray diagram is similar to the process of concave mirror, but you have to extend lines to the back of the mirror.
    • convex_mirror_sample.JPG

Refraction of Light
  • During the light wave is travelling, if the light wave met new medium to pass through, the refraction occurs and change its velocity and wavelength.
  • Due to these changes the light path will bend.
  • The changes will vary to the dense of medium.
  • ex_refraction.JPG
    This kind of events will happen due to refraction of light that is travelling toward your eyes
  • If the light wave pass the new medium with perpendicular angle with boundary, the bend of path will not happen
  • The speed of light is depend on optical density
  • The optical density also determine the index of refraction of the objects that can be the media of light
  • The mathematical formula of index of refraction is n = (speed of light) / (speed of light in the object)
  • Normal line represents the line that is perpendicular with the material that light will refract when it pass through
  • If incident ray has faster speed and have slower refraction ray, which means slow down speed during refraction, the light will bent toward normal line.
  • If incident ray has slower speed and have faster refraction ray, which means fast speed up during refraction, the light will bent away from normal line.
  • Leatst time principle stated that light will always choose the path that can move in shortest time.
    • It can be compared to the life guard because when they try to save a drawn person, they always should take way that has shortest time to reach to drawn person.
  • During refraction, the bend of path will not occur when the light comes along the normal line with 0 degree.
  • Snell's law stated that (index of refraction of original medium) * sin(angle that incident ray pass to the other medium) is equal to (index of refraction of the other medium that light pass through) * sin(angle that make with normal line after the bent of light wave due to refraction)
  • With snell's law you can solve many problems that involves refraction, such as the angle of incidence and angle of refraction
  • If ni = nr, angle of incidence and angle of refraction
  • if ni is bigger than nr, angle of incidence is smaller than angle of refraction
  • if ni is smaller than nr, angle of incidence is bigger than angle of refraction
  • (n1)/(n2) = wavelength 2 / wavelength 1


Answers
1. What is concave Mirror?
  • Concave mirror is one of the type of spherical mirror and it have silver on the inside of the shpere.
2. What is convex Mirror?
  • Convex mirror is one of the type of spherical mirror and it have silver on the outside of the shpere.
3. What is the relationship between index of refraction and refraction angle
  • The index of refraction and refraction angle are directly related.
4. What is snell's Law?
  • Snell's law stated n1 * sin(angle of incidence) is equal to n2 * sin(angle of refraction).
5. What is index of refraction?
  • Index of refraction determined by optic density and it determines how much the light will bent when the light pass through the material.

Lab: Curved mirrors


Objective: Demonstrate the focal properties of spherical reflecting surfaces

Data

Object Distance (cm)
Focal Length (cm)
Calculated Image Distance (cm)
Experimental Image Distance
(cm)
48
5
5.5
5.4
18
5
6.9
6.6
23
10
17.7
17.3
48
10
12.6
12.6

concave_mirror_lab_data.jpg
Convex_mirror_lab_data.jpg

Questions

  1. How does the measurement of the focal point found for the convex mirror relate to the focal point found for the concave mirror?

  • Focal point of convex mirror and focal point of concave mirror had similar value, approximately same value of length.

  1. How well did your image characteristics agree with the predicted descriptions?

  • It had slight error about 0.2cm however it almost agreed the predicted description

  1. Why were you not asked to determine whether the images were real or virtual?
  • Because convex mirror always produce virtual image and it doesn't matter to the result of this lab.

LAB: Refraction of light through glass


Objective: What is relationship between Sine of incidence angle and sine of refraction angle?
Hypothesis: the sine of incidence angle and sine of refraction angle are directly related.

DATA
Angle of Incidence (air) (°)
Angle of Refraction (Glass)(°)
Sin ᶿi
Sin ᶿr
ᶿi- ᶿr (°)
ᶿi/ ᶿr
nr
% error(%)
10
8
0.174
0.139
2
1.25
1.25179856
17.644832
20
16
0.342
0.276
4
1.25
1.23913043
18.478261
30
22
0.5
0.375
8
1.36364
1.33333333
12.280702
40
27.5
0.643
0.462
12.5
1.45455
1.39177489
8.4358624
50
33
0.766
0.545
17
1.51515
1.40550459
7.532593
60
37.5
0.866
0.609
22.5
1.6
1.42200328
6.4471524
Refraction_of_light_lab_data_chart.jpg
Data_for_refraction_of_light_through_glass.jpg

Analysis Question
1) How does the angle of incidence compare to the angle of refraction when light travels from a medium of low optical density (air) to a medium of high optical density (acrylic)?
  1. Choose one: always smaller, always bigger, or always constant.
  2. Provide evidence from the lab.
    • The angle of incidence was always bigger than the angle of refraction when light travels from a medium of low optical density to a medium of high optical density. For example, when the angle of incidence was 10 degree, the angle of refraction was only 8 degree. Also during the lab, the light bent toward normal.

2) How does the angle of incidence compare to the angle of refraction when light travels from a medium of high optical density (acrylic) to a medium of lower optical density (air)?
  1. Choose one: always smaller, always bigger, or always constant.
  2. Provide evidence from the lab.
    • The angle of incidence was always smaller than the angle of refraction when light travels from a medium of high optical density to a medium of lower optical density. For example, when the angle of incidence was 10 degree, the angle of refraction was only 8 degree however, at the end, when the light completely pass the glass, it went back to 10 degree. Also during the lab, the light bent away from normal.

3) What would happen to a light that entered the acrylic along the normal?
  1. The light refracted towards the normal.
  2. The light refracted away from the normal.
  3. The light only reflected off the plate.
  4. The light did not refract, but went straight.

4) Discuss how the angle of refraction changed with the angle of incidence. As the angle of incidence increased, the angle of refraction
  1. Increased.
  2. Decreased.
  3. Remained the same.
Analysis

The sine of incidence angle and sine of refraction angle are directly related. The slope of the equation of the graph is 1.3854, which represent the index of the refraction. The percent error with the actual value of index of refraction of glass, about 1.52, whas approximately 9 percent.

The interesting animation about relection from boundry
reflection_against_wall.jpg
http://faraday.physics.utoronto.ca/IYearLab/Intros/StandingWaves/Flash/reflect.html
This shows the wave that reflected by wall

Lesson 3:Total Internal Reflection & Lesson 4: Interesting Refraction Phenomena & Lesson 5: Image Formation by Lenses & Lesson 6: The Eye


Summary
Question
1. What is critical angle?
2. What is dispersion?
3. What is Total internal reflection?
4. What are the types of lenses?
5. How the eyes work?
Total Internal Reflection
  • Discrepant event: The situation when the incident ray pass the first boundary of triangular block without refraction along the normal line and when it reach the second boundary of triangular block, the reflection happens.
  • The reflection event that occured in the discrepant event is called total internal reflection
  • This phenomenon happens when the angle of refrection is greater than 90 degree, when incident angle is bigger than its critical angle and when light is moving from more dense to less dense.
  • When TIR happens, all the energy of incident ray will bounce off and stay to first medium
  • This proves obtical fiber
  • Discrepant_event.jpg
Critical Angle
  • Value of angle of incident that makes refraction angle as 90 degree
  • The mathematical equation is inverse sine( nr / ni)
Dispersion
  • Dispersion is the event that the visible light is seperating into 7colors: ROYGBIV.
  • Each color has different frequency
  • Dispersion occurs due to index of refraction value which depend on its frequency
  • Angle of deviation represents the angle between the incident ray and refracted ray
  • Red light refract least and Violet light refract most
  • Rainbow is dispersion that causes by droplet and sunlights
  • Rainbow water particles are capable to make angle of deviation in 40-42 degree therefore the rainbow looks like half circle
  • path_of_rainbow.jpg
Mirage
  • Mirage is an illusion that is created by difference of air temperture that results refraction.
  • It usually observed at sunny weather or hot weather.
  • It is an rare event in common life
Lenses
  • anatomy_of_lenses.jpg
  • Material that refracts light ray
  • Focal point represents the point where the light that passed the lenses focuses. In Diverging lenses, it is at back ward.
  • Principle axis is the imaginary horizontal line that passes through the center of sphere of the lenses
  • Vertical axis is the imaginary vertical line that passes through the half of the double lenses.
  • 2F point is the point where it has length of twice of focal length from the lense.
  • Focal length is the length between focal point and lens' surface that refraction happens.
  • Equations are identical with mirrors
    • (1/f) = (1/do) + (1/di)
    • (hi / ho) = -(di / do)
  • There will be no net affact when the incidence ray passes through the centerpoint
  • There is two types of lenses
    • Converging Lenses
      • Invovles convex lens and double convex lens
      • Any incident ray that is parallel to the principle axis of converging lens will refract toward the focal point
      • Any incident ray that passes trough the focal point and converging lens, the refracted ray is parallel to principle axis
      • When the incident ray first pass the first boundary, it is moving fast to slow therefore the refraction ray will bend toward normal line and when the ray pass through the second boundary, it is moving slow to fast therefore the refraction ray will bend away from normal line
      • When an object is at behind 2f point, the reduced inverted real image will from at position between 2f point and f point at the other side.
      • When an object is at 2f point, the same size inverted real image will form at 2f point on the other side.
      • When an object is between 2f point and focal point, the enlarged inverted real image will form at behind 2f point on the other side
      • When an object is at position that is closer to the lens than focal point, the enlarged upright virtual image will form behind 2f point on the same side
      • When an object is at focal point, no image will form.
      • How to draw ray digram of converging lens
      • drawing_ray_diagram_of_converging_lens.jpg
    • Diverging Lenses
      • Involves concave lens and double concave lens
      • Any incident ray that is parallel to the principle axis of diverging lens will refract the direction of its focal point. When you draw extended line, the line will pass the focal point
      • Any incident ray that is directed toward the focal point of diverging lens will refract as parallel line to principle axis
      • When the incident ray first pass the first boundary of diverging lens, it is moving slow to fast therefore the refraction ray will bend away from normal line and when the ray pass through the second boundary, it is moving fast to slow therefore the refraction ray will bend toward normal line
      • Always form uprighted reduced virtual image in front of the diverging lens.
      • How to draw ray diagram of diverging lens
      • ray_diagram_of_diverging_lens.jpg
The Eye

  • anatomy_of_the_eyes.jpgEyes are filled with fluids
  • Cornea: Opening of eyeball, Refract light. Protection
  • Pupil: Opening after the light came through the cornea
  • Iris: It controls the size of pupil., colored part of eye. It re,duces openning in bright situation
  • Crystalline lens: made of layers of fibrous, index of refraction is approximately 1.4, double convex lens
  • Ciliary muscles: Helps to change the shape of lens to change the focal length
  • Retina: detects intensity and frequency of lights with rods and cones
  • Optic nerve: Network of nerve cells that connects the brain and eye.
  • Fovea Centrails: the region that has greatest conpacted rods and cones
  • Focal length of eye is about 1.8 cm
  • Accommodation represents the skills and abilities of eyes to adjust the focal length
  • The measurement of power of lens is diopter.
  • Diopter is equal to 1/ focal length
  • Power of accommodation represents the maximum variables of diopter
  • Farsightedness or hyperopia is that the eye is not capable of focus on the object that is near to the eyes. To correct the problem, you need to put convex lens on the front of your eyes
  • Farsightedness.jpg
  • Nearsightedness or myopia is that the eye is not capable of focus on the object that is far from your eyes. To correct the problem, you need to put concave lens on the front of your eyes


  • Nearsightedness.jpg

Answers
1. What is critical angle?
Angle of incidence that forms 90 degree of angle of refraction
2. What is dispersion?
Dispersion is seperation of visible light by refraction of light and you can see different colors
3. What is Total internal reflection?
Total internal reflection is the situation when the angle of incidence is greater than critical angle and only relection happens rather than the refraction.
4. What are the types of lenses?
There are concave lens(deverging lens) and convex lens(converging lens)
5. How the eyes work?
The light passes through Cornea and pupil then refract when it passes through the lens and touch the focal point of lens, retina, which is connected to nerve system.

LABS: Prism
Objective: To show how a prism separates white light into its component colors and to show that different colors are refracted at different angles through a prism

Analysis questions
1) What colors are seen exiting the prism and in what order are they?

  • Red - Orange - Yellow - Green - Blue - Indigo - Violet

2) Which color is refracted by the prism at the largest angle?

  • Violet

3) Which color is predicted to refract at the largest angle? Did your experimental results match the theoretical predictions?

  • Violet, Yes my experimental results match the theoretical predictions.

4) Do the colored rays emerge from the Prism parallel to each other? Why or why not?
  • No They are not parallel to each other becase they had different refraction angles.

LAB: Lenses
Objective:To precisely determine the focal length of a thin lens. To verify the image characteristics formed when objects are placed at varying distances from a lens.
Hypothesis: 1/f = 1/di + 1/ do

DATA
Lens_Lab_Data.jpg


Calculation
1. Distance of image calculation
(1/f) = (1/di) + (1/do), di = (1/f - 1/do)^-1,
sample: (1/5 - 1/20) ^ -1 = 6.67
2. Height of image calculation
hi/ho = -di/do
hi = (-di/do) * ho
sample: (-6.67 / 20) * 4 = -1.4


The interesting animation for lens
lens_applet.jpg

http://faraday.physics.utoronto.ca/IYearLab/Intros/LensOptics/Flash/ObjImage.html

This animation helps to understance the relationship between the location of object and image that is created by lens.