Physics 2204
Unit 4
4.01 Introduction to Waves
_____________: Repeated oscillation about some equilibrium point. Vibrating objects undergoing simple harmonic motion (SHM) can create waves.
_______________: is a single traveling disturbance caused by a vibrating source. A wave can be thought of as a series of repeated pulses.
_____________: A transfer of energy in the form of a traveling disturbance caused by a vibrating source. Some waves require a medium in which to travel. (sound, water waves, etc) while others do not. (Radio waves, x-rays, etc). For example, in a water wave the waves carry ______________b/c of the disturbance of the _________________which is water.
__________________: The number of complete cycles of a wave which pass a point in a given time. Frequency, f, is usually measured in cycles per second, or Hertz, Hz. 60 Hz means that 60 waves pass a point in each second.
______________: The amount of time for one complete wave to pass. Period, T, is measured in seconds.
__________________: The displacement of the particle from the rest position is its amplitude, A, measured in meters. Generally, when we say amplitude we are referring to max amplitude.
______________: Two particles can be said to be in phase if they are at the same amplitude and moving in the same direction.
________________: The distance from one point in phase to another point in phase.
_______________: A cycle is one complete wave. The length of a complete cycle is the
wavelength (λ) while the time for one complete cycle is the period (T).
Ex: A pendulum completes 30 cycles in 15 seconds. What is its period and frequency?
Assign:
4.02 Transverse and Longitudinal Waves
Waves and Energy
The energy of a wave depends on the type of wave.
A mechanical wave’s energy is proportional to the square of its _________________just like a vibrating object in_________________________________. (E = KA2).
It has nothing to do with frequency. (ex: water waves, slinky waves). ______________________ transfer energy through the motion of their particles. As the particles move they interact with adjacent particles creating a domino sort of effect.
In energy waves, the energy depends on __________________. (ex: light)
This “ripple” of energy travels from the origin to distant places. (Depending on the damping it experiences).
Some waves are capable of traveling vast distances...such as light in outer space, earthquakes here on earth, and tsunami on the ocean floor.
There are two types of waves that we will be studying: ___________________and _____________________.
Waves in which the particles are vibrating _________________to the motion of the wave. Examples include light and waves on a string. A ____________________is a single incidence of this.
_________________________:
Waves in which the particles are vibrating ________________to the direction of the wave's motion. Examples include sound and some slinky waves. A ___________________________is a single incidence of this.
Reflection of pulses:
When a pulse hits a fixed end (attached to a wall) it reflects back ___________________.
When a pulse hits a free end (not attached) it reflects back on the______________________.
4.03 Universal Wave Equation
The Universal Wave Equation:
Ex:
a) Calculate the period and frequency of a tuning fork whose tines vibrate back and forth 385 times in 2.81 seconds.
b) Calculate the speed of the sound wave leaving the tuning fork if the wavelength of one cycle is 255 cm.
p. 477 #2, 6, 23, 24, 26, 27 Read p. 382 - 389
p. 445 - 449
Practice set - Waves
Practice Set - Waves
You may need to read your text p. 382 - 389 and p. 445 - 450 or check your notes.
The two general types of waves are _____________ and ______________. All waves are created by a __________________ and involve the transfer of _____________. In a longitudinal wave the particles vibrate ______________ to the direction of wave propagation. In a transverse wave the particles vibrate _____________ to the direction of wave propagation. Another word for vibration is an
______________. A transverse wave has positive pulses called __________ and negative pulses called ____________. The distance from one point in-phase to another point in phase is called the
__________________. The Greek symbol for this is ____________. The maximum displacement from the rest position of a wave is called the _________________. An example of a longitudinal wave is _______________. An example of a transverse wave is __________________. A longitudinal wave is made up of _________________ and rarefactions. The amount of time required for one complete wave to pass is called the ___________. The symbol for this is ___________ and it is measured in
__________. The number of cycles passing a point in a given time is the _______________ measured in ______________. Waves which require a medium to travel are called matter waves. An example of these are _________________. Some waves do not require a medium in which to propagate. An example of these are ____________________.
1. A child swinging on a swing vibrates with a constant amplitude of 1.2 m. Draw 3 - 4 diagrams representing the child going through one complete cycle.
2. State the type of vibration in each case. (transverse or longitudinal) a) A jackhammer is used to crush a roadbed.
b) The beak of a woodpecker swings back and forth.
3. A pendulum swings side to side and in one complete cycle covers 8 meters. What is the amplitude?
4. Calculate frequency in hertz and period in seconds for each of the situations below. a) A film slide operates at 64 frames per minute.
b) George eats 3 square meals a day. c) Sally takes out the garbage once a week. d) A patient's pulse rate is 72 Beats per minute
5. Calculate the period of vibration in seconds if the frequency is
a) 0.23 Hz b) 5.2 MHz c) 3.6 x 10-7 Hz
6. Calculate the frequency in hertz of an object that vibrates with a period of a) 0.003 s b) 4.7 x 10-4 s c) 6 hours
7. Draw a periodic transverse wave consisting of 2 wavelengths with A=3.0 cm and λ=2.0 cm. Be sure to label the wavelength, crest, trough, and amplitude.
8. Draw a periodic longitudinal wave consisting of 2 wavelengths with λ=2.0 cm. Be sure to label a compression, a rarefaction and a complete wavelength.
9. Draw diagrams illustrating the reflection of a pulse from a: a) free end
b) fixed end
1 diagram 6a 333 Hz
2a longitudinal 6b 2130 Hz
2b transverse 6c 4.63 x 10- 5 Hz
3 2.00 m 7 diagram
4a 1.07 Hz, 0.935 s 8 diagram
4b 3.47 x 10- 5 Hz, 2.88 x 104 s 9a diagram
4c 1.65 x 10- 6 Hz, 6.06 x 105 s 9b diagram 4d 1.20 Hz, 0.833 s 10 notes 5a 4.35 s
5b 1.90 x 10- 7 s
4.04 Transmission and Speed of Sound
The Creation of Sound
All sound is created by a ____________________source.
Ex: The vibrating of your voice box, a guitar string, or a ringing bell.
The sound then travels as a ___________________matter wave, which requires a medium through which to travel.
Factors Affecting Speed of Sound:
Sound travels at different speeds at different times, so these are some of the factors affecting the speed of sound.
1. ____________________________ 2. ____________________________ 3. ____________________________
Type of Material:
Sound travels as a series of compressions and rarefactions in the molecules of the medium through which it is travelling.
The _____________ the material, the faster the speed of sound, because the molecules are held together more rigidly.
Density of Material:
The closer together the particles, the easier it is to____________________, so denser materials usually transmit sound _______________ than less dense materials. This is not always the case however.
Temperature:
Since sound is caused by the bumping together of particles, if the particles are moving faster (higher temperature) the energy will be transmitted ____________. Thus sound travels faster in warm air than in cold air.
Equation for the speed of sound in air:
v = 332 + 0.6T Where T = temperature. (°C)*This assumes that the pressure of the air is constant.
Example: If it is 10° outside, what is the speed of sound?
Estimating Distance from lightning:
Because sound is so much slower than light, we can tell how far away a lightning strike is by comparing the sound of the thunder to the sight of the lightning.
Ex: Lightning strikes and you count slowly to 9 before you hear the thunder. The lightning is ~ 3 km away from you.
Assign:
read p. 450-452 do p. 453 #1-3
4.05 Doppler Effect
Warmup
What must be the temperature if the speed of sound in air is 348 m/s?
Doppler Effect:
The apparent change in frequency of a sound when the source is moving.
To an observer in front of the moving sound source the frequency seems higher, while behind the source the frequency seems lower.
Doppler Equation
f2 = _____________________________
f1 = _____________________________
vs = _____________________________
vo = _____________________________
* for a stationary observer and a moving source use + for a receding sound
use - for an approaching sound
_____________________ is the difference in frequencies f2 - f1
Note:
+ shift means approaching - shift means receding
Ex 1: Julian is approaching Nick at 140 km/hr, screaming at 500 Hz.
a) What frequency does Nick hear if the speed of sound is 344 m/s?
The Doppler equation can also be applied to light waves. The only difference is that we use v light = c = 3.00 x 108 m/s instead of v sound.
Ex 2: A distant galaxy is moving away from the earth at a speed of 6.25 x 106 m/s. It emits light with a wavelength of 580 nanometers (580 nm = 580 x 10-9 m) If the speed of light is
c = 3.00 x 108 m/s, what is the wavelength of light that is detected on earth? What is the Doppler shift?
Mach Number and the sound barrier
Some aircraft can approach or break the speed of sound in air (approximately 332 m/s or 1195.2km/hr)
When they do this, a new unit is used to describe their speed. This unit is the _______________
Mach 1 is defined as the speed of sound at a given temperature. Speeds ≥ Mach 1 are __________________
Speeds < Mach 1 are __________________ Speeds ≥ Mach 5 are __________________
Ex 2: How fast is a jet moving if it is 40° C outside and the Mach # is 1.8? 1. Find v sound first using temperature
2. Find v jet using Mach number
Assign:
read p. 453 - 457 Do p. 458 #1 – 3
p. 467 #3 Answers to 3 are incorrect: 413.2 Hz 493.9 Hz
Assume v sound = 343 m/s
p. 480 #64 - 66, 69
f
f v
v
v
s s
0 0Practice Set - Sound, Mach #, Doppler
Speed of sound in air is defined by v = 332 + 0.6 x (T)
1. What is the temperature of the air if the speed of sound is: a) 348 m/s (27° C)
b) 1200 km/hr (2.2° C)
2. What is the speed of sound if the air temperature is: a) 7.5° C (337 m/s)
b) 32° C (351 m/s)
Mach number is defined as v = speed of sound x Mach number
3. What is the speed of a jet flying Mach 3 when: a) the speed of sound is 332 m/s? (996 m/s) b) the air temperature is -11 ̊C (976 m/s)
Doppler effect is defined as the apparent change in frequency heard when a source is moving relative to an observer. The equation is:
4. A race car is approaching a stationary observer at a speed of 210 km/hr emitting a sound with a frequency of 875 Hz. What frequency does the stationary observer hear if vsound = 343 m/s? (1054 Hz)
5. How fast must a police car be travelling if an observer hears 1100 Hz from the siren when the actual sound is 1200 Hz if the speed of sound is 343 m/s? Is the car moving away from or towards the observer? (31.2 m/s)
Doppler effect is also observed with light as distance galaxies move away from earth. To find the speed of the distant galaxies, use the Doppler equation, but instead of vs, use c = 3.00 x 108 m/s
(the speed of light)
6. A distant galaxy is receding at 3.45 x 107 m/s from earth. It emits light with a frequency of 4.70 x 1014 Hz. What frequency of light is detected on earth? ( 4.2 x 1014 Hz)
Sometimes you will be given the wavelength instead of the frequency of light. Convert using the universal wave equation (v = fλ). Recall that 550 nm = 550 x 10-9 m.
7. A distant galaxy approaching earth at 2.77 x 107 m/s emits light with a wavelength of 682 nm. What wavelength of light is detected on earth? (619 nm)
4.06 Intensity and Intensity Level
Warmup:
Find the speed of a jet which travels at Mach 1.5 when the speed of sound in air is 332 m/s.
Sound Intensity:
The power P, of the wave in Watts (W) that passes through an area A in (m2).
Humans can hear sound intensities ranging from 10-12 W/m2 (threshold of hearing) up to 1.0W/m2 (threshold of pain)
As you get further from the source, the sound intensity drops off as an inverse square law, just like with the law of gravitation...
Mathematically we can say:
Where: I = ____________________________
Ex1: A sound has an intensity of 3.2 x 10-5 W/m2 at a distance of 1.8 m from a sound source.
What is the intensity of this sound at a distance of 3.6 m?
Ex 2: A sound wave is created from a stationary source. If the first listener is 700 m away and the second listener is 1000 m away by how much has the intensity decreased by the time it reaches listener 2?
Sound Intensity Level:
Because of the huge range of human hearing, Sound intensity is a bad scale to use. Instead we use a _______________________ to measure units of sound intensity.
The __________________, is defined by:
Where: β = ____________________________
I2 = ____________________________
I1 = ____________________________
Because the Decibel scale is exponential the intensity of a 10 decibel increase is actually 10 times as great!
Assign
read p. 458 - 462 do p. 462 # 1 - 2
Page 24 of 52
I
I
r
r
1 2 2 1 2
Practice Set - Intensity and Intensity Level
Intensity is defined as the amount of sound power per unit area. I = W/m2. 1. What is the threshold of hearing?
2. What is the threshold of pain?
Inverse Square law a relationship which describes what happens to sound intensity as the distance from the source changes. If the distance doubles, the intensity divides by 4. If the distance triples, the intensity divides by 9.
3. By what factor does the intensity change if the distance from the source changes from 2.0 m to 6.0 m?
4. A sound has an intensity of 2.8 x 10-6 W/m2 at a distance of 6.2 m from a source. What must be the new distance if the sound has an intensity of 3.7 x 10-9 W/m2? (171 m)
Intensity level uses the deciBel (dB). It is a logarithmic scale. Each 10 decibels is 10 times as loud in intensity.
5. By what factor must the sound intensity change if the intensity level changes from 20dB to 60 dB?
Page 25 of 52
4.07 Hearing
Sensitivities to Sound:
The human ear can detect sound intensities ranging from 1.0 x 10-12 W/m2 (1.0 pW/m2) all the way up to 1.0 W/m2, ranging from _________________________all the way to
________________________.
This sensitivity is dependent on the frequency of the sound. see p. 470.
Put another way, if a flute and a tuba were emitting the same intensity, the flute would seem louder to us.
We can hear frequencies ranging from 20 Hz to about 20000 Hz. However, the ear is most sensitive to frequencies between 1000 Hz and 5000 Hz. This is known as the
___________________.
Sounds above 20 000 Hz are _________________while those below 20 Hz are known as _________________.
Comparing Intensity and Intensity Level
Page 26 of 52
Applications of Sound:
__________________________: sonar stands for Sound Navigation and Ranging
__________________________: Used to find flaws in materials like tires and welds. Short bursts of sound fired into the material and reflecting vibrations are analyzed.
__________________________: Used to keep things mixed that don’t normally mix, like the fat in milk.
__________________________: Used to clean gems and other materials.
__________________________: Ultrasounds create a fine mist to humidify dry rooms (not a problem in NF usually)
__________________________: Used as a safer way to observe babies and organs you would rather not bombard with x-rays.
__________________________: Used to break up kidney stones in a non-painful procedure.
Page 27 of 52
4.08 Superposition
The Superposition Principle:
Two or more waves can move through each other. Sound waves travel as ______________waves but we usually represent them as ___________________ waves because these are easier to draw.
____________________is the result of two or more waves meeting at a particular point in space at the same time.
The net wave which forms at the point of interference has an amplitude that is equal to the vector sum of all the wave amplitudes that come together at that point.
This concept of adding up the amplitudes is called the_________________________.
Superposition in pulses:
______________________: resultant displacement is greater. _______________________: resultant displacement is smaller.
If two waves are exactly the same and they meet, the result is sometimes called
______________________, because the two waves totally cancel each other out. However, they pass through each other and continue travelling in the original direction.
Page 28 of 52
Waves and Matter:
When waves meet a different kind of matter they can be either _______________, ________________, or ____________________.
_____________________: the waves energy is dissipated or turned into other kinds of energy. (Sound waves and sound proof rooms, water waves and breakwaters)
_____________________: the wave travels on through the new substance. (light waves through glass, microwaves through paper, x-rays through skin)
* some energy may be absorbed in the process
* change in wavelength because the speed of the wave changes
_______________________: the wave rebounds off the surface. (light waves off a mirror, sound waves off a canyon wall)
* recall that pulses reflect differently from ___________________ and ___________________
Assign:
Page 29 of 52
4.09 Standing Waves
Standing Waves:
Standing waves are a special case of_________________. When two waves with the same frequency travelling in the same medium meet, this interference pattern will be created.
It is very difficult to generate two waves of exactly the same frequency, so this is usually observed when an incident wave meets its reflection.
When this occurs, there are areas of constructive interference called ________________ and areas of total destructive interference called ______________.
Standing Waves in Strings:
Fundamental
____________________ n=1 ____________________
1st Overtone
_____________________ n= 2_____________________
2nd Overtone
_____________________ n= 3_____________________
Page 30 of 52
________________________ is the distance between two nodes.
Ex: A standing wave is produced on an 8.0 m long string in the 4th resonance. The frequency of the vibrating source is 400 Hz.
a) Draw the wave
b) Find the wavelength (there are three ways)
c) Find the speed of the wave
Assign:
Page 31 of 52
4.10 Mechanical Resonance
Mechanical Resonance
__________________: All objects have a frequency at which they vibrate most easily. This is called the ___________________.
_______________________: The vibrating response of an object to a periodic force from a source that has the same frequency as the natural frequency of the object.
If we can match the natural frequency, we can get the object to vibrate.
Examples of Mechanical Resonance:
Resonance of large buildings with earthquakes cause them to fall down.
Getting a car out of a snow bank
Pushing a child on a swing
Pendulum clocks
“Sweet spot” in a baseball bat
Peach making a grease bucket run
Acoustic Resonance and Musical Instruments:
Know your ____________rule“There is a node at any fixed end and an antinode at any open end reflection.” Remember fixed and free end reflection?
We know that standing waves can only exist at certain frequencies.
These frequencies correspond to different lengths of the air column in wind instruments. These are called _______________________.
Page 32 of 52
Air Columns Open at Both Ends
Fundamental
_______________________ n=1 _______________________
1st overtone
________________________ n=2 ________________________
2nd overtone
________________________ n=3 ________________________
Page 33 of 52
Ex: A standing wave is set up in a 2.5 m long pipe with both ends open. If the speed of sound in air is 332 m/s, what frequency is required to create the second resonance?
Air Columns Closed at One End
Fundamental___________________ n=1 ___________________
1st overtone
___________________ n=3 ___________________
2nd overtone
___________________ n=5 ___________________
Page 34 of 52
Ex: A standing wave is set up in an air filled column closed at one end. The air temperature is 20° C and a 440 Hz tuning fork is held near the open end. What length of tube is needed to hear the 3rd harmonic?
Assign
read p. 494 - 504 do p. 505 # 1, 2
Page 36 of 52
4.11 Beats
Beats
Refers to the frequency of a_____________________, and not the frequencies of the individual sounds which make up the noise.
As the sound waves from each wave travel, the slight frequency variation leads to a pattern of _________________and __________________interference which results in us hearing beats.
beat frequency:
Example: Calculate the beat frequency when a tuning fork of 440 Hz is sounded with one of 442 Hz.
Assign: read p. 510 do p. 435 # 29 - 35
do p. 477 # 23, 30, 35 - 40, 44, 45, 49 do p. 480 # 56abc, 60, 64
do p. 511 # 1 do p. 515 # 2 - 6
Page 37 of 52
4.12 Intro to Light
Light Theory
Light Propagation (travel)
Light is an ______________________wave; made up of vibrating _________________fields and _____________________fields. As the electric field vibrates it causes a magnetic field to vibrate which causes an electric field to vibrate etc. etc.
See Figure 10.4 p. 386
Since electric fields and magnetic fields can exist in a vacuum, light needs _________________ to travel.
How fast is light?
Today’s accepted value for the speed of light, c is:
Is light a wave or a particle? We will see it sometimes acts as a bit of both.
How does light travel?
Light travels in a straight line (usually)
This is called_______________________. The shadows we see behind flagpoles gives us good evidence of this.
Page 38 of 52
A _____________________is a stream of light rays and is represented by a number of rays. The rays may be ___________________, __________________, or _________________.
Electromagnetic Theory
- Light (or visible light) is simply one kind of __________________________________.
Diverging Rays Converging Rays Parallel Rays
(flashlight) (magnifying glass) (laser)
Beam Beam
Assign:
Read diagram p. 393
note: all these forms of energy obey the universal wave equation v=fλ
Read p. 390-393
Do p. 393 #1-2 (1 pm = 1 x 10-12 m)
Page 39 of 52
4.13 Light Properties
Warmup:
What is the frequency of light which has a wavelength of 550 nm? (1 nm = 1 x 10-9 m)
Light Properties
____________________: Light passes through some materials. As it does it may lose some energy (heating up the medium) and slow down.
___________________: As a wave passes through a narrow slit it will bend to fill the space behind it. In order for this to happen, the slit must be around the same size as the wavelength. Ex: Water waves
Page 40 of 52
Reflection: Light will bounce off certain objects. If the object is smooth enough
________________ reflection occurs and you can see your reflection. If the object is rough, __________________reflection occurs, and an image can’t be seen.
_______________________states that the angle of incidence must equal the angle of reflection.
θi = θr
Images in Plane Mirrors: (Flat mirrors)
Images in plane mirrors are ___________________and ________________ (they can’t be projected onto a screen). As well, images undergo ____________________(left and right are switched).
Page 41 of 52
__________________: The bending of light as it passes from one optical medium to another. Ex: A straw in a glass of H2O
θ1 > θ2
The light must slow down
and bend towardsthe normal line
Locating an Image in Plane Mirrors:
1. Draw incident ray from object to mirror, and reflected ray from mirror to eye. Obey Law of Reflection.
2. Extend reflected ray behind the mirror (dotted line)
Page 42 of 52
θ1 < θ2
The light must speed up
and bend away from the normal line
Index of Refraction
A measure of the speed of light in a medium when compared to air. Where: n = _______________
c = _______________ v = _______________
Examples:
nquartz = 1.6 ndiamond = 2.42
vlight = 1.88 x 108 m/s vlight = 1.24 x 108 m/s
*higher n values means slower light
Assign:
Page 43 of 52
4.14 Snell’s Law
Snell's Law
If n1 > n2 we can find the________________, θc, at which ________________________occurs.
Page 44 of 52
b) Light travels from water (n = 1.33) into quartz (n = 1.67). If the angle of incidence is 58°, find the angle of refraction.
c) If the light travels instead from quartz into water, find the critical angle.
Practice:
Light travels from glass (n = 1.55) into quartz (n = 1.67). If the angle of incidence is 48°, find the angle of refraction.
1. Sketch diagram
Page 45 of 52
Applications of Total Internal Reflection
Rainbow (see p. 415)
incident sunlight is ____________________split into its separate colours) it then internally reflects inside a water droplet to produce the rainbow we see.
Fibre - Optic Cable (see p. 411)
Light is sent through glass fibres at an angle greater than the critical angle.
All the light __________________ reflects. This allows for information to be passed at great volume with little signal loss. (internet connections)
_________________________: A long flexible plastic tube can be inserted into the body to examine you without cutting you open.
Page 46 of 52
________________: Warm air is less dense than cool air, so light travelling near a hot
surface will totally internally reflect. You see an inverted palm tree, and the sand looks like water._____________________: Most rays entering the top of the diamond will internally reflect until they reach the top face of the diamond where they exit.
Assign:
Read p 407 - 412 p 404 # 1-2
p 407 # 2 (see p. 405 for n values) p 413 # 1
Day 2
Read p 414 - 418
p 436 #37, 40, 41 (answers are wrong) p 438 #57, 59, 64, 66, 67, 79
Page 47 of 52
4.16 Light Interference
Warmup
Light is incident in quartz (n = 1.67) onto water (n = 1.33).
a) What is the critical angle for quartz into water?
b) If light refracts at 72°, what was the incident angle?
Interference of Light Waves
Like other waves, light waves can interfere with each other.
This interference can be either ____________________ (bright lines called ____________) or __________________ (dark lines called __________________).
In order to get light waves to interfere it is easiest to cause light to __________________ through very narrow slits.
As long as the size of the slit is close to the size of the light wavelength, the light will diffract and form an ____________________________ (see p. 430)
Page 48 of 52
Thomas Young's sketch of two-slit diffraction, which he presented to the Royal Society in 1803
Single Slit interference
Gives the location of the _______________(nodal lines.) The calculation:
Where: n: _____________________________
λ: _____________________________
w: _____________________________
θn: _____________________________
Page 49 of 52
Example 1:
A single slit with a width of 1.7 x 10-5 m is illuminated with red light with a wavelength of 660 nm. At what angle does the 2nd order minima occur?
Double Slit interference
Gives the location of the maxima (bright lines)
The calculation: n: ___________________
λ: ___________________
xn: ___________________
θn: ___________________________
d: ____________________________
L: ____________________________
Page 50 of 52
Example 2: Double Slit Maxima
A 550 nm light source illuminates double slits that are 3.0 x 10-6 m apart. For a screen that is 0.9 m away from the slits, how far will the first order maxima (n = 1) appear from the
centerline?
Assign:
Read p. 424 - 431 Do p. 429 #2a, 3 431 #2b
441 #100 a, 101 STSE #4
Page 51 of 52
n
1sin
1
n
2sin
21sin c 2sin 90
n
nPractice Set #12 - Light
The Index of Refraction, n, is a measure of the optical density of a material.
n = c v
1. What is the index of refraction if the speed of light in a medium is 2.72 x 108 m/s. (1.10)
Snell’s Law is used to calculate the refracted angle when light passes from one medium to another.
2. Light in water ( n = 1.33 ) has an incident angle of 42°. What will be the angle of refraction if the second medium is
a) glass ( n = 1.67 ) (32.2°) b) air ( n = 1.00 ) (62.9°)
If the material travels from a dense medium to a less dense medium it may totally internally reflect. This only occurs when θ2 = 90° and θ1 is called the critical angle.
3. For light travelling from crystal ( n = 1.89 ) into water ( n = 1.33 ) calculate the critical angle. (45°)
Page 52 of 52
n
d
dx
L
n
sin
sin nn
w
Single Slit Diffraction Pattern occurs when light is shown through a narrow slit.
n = number of minima λ = light wavelength (m) w = slit width (m) θn = angle (°)
4. At what angle will the second order minima occur if light with a wavelength of 578 nm is shown on a screen with a slit of width 1.23 x 10-6 m? (70°)
Double Slit Interference patterns occur when light is shone though two narrow slits.
n = number of maxima λ = light wavelength d = slit separation (m)
θn = angle (°)
x = distance from center to max L = distance from slit to screen 5. Monochromatic light of wavelength 495 nm shines on a pair of slits. The screen is 1.3 m away
and the distance between the 9th bright line and the centre line is 3.0 cm. Find the slit separation. (1.93 x 10-4 m)
This is the end of Unit 4 – Waves. You are now finished the year. Congrats.
