Solutions Topic 4 Part 2
1. Wave Phenomena : Reflection and Refraction
http://www.physicsclassroom.com/Class/waves/
Check Your Understanding
Case 1: A pulse in a more dense medium is traveling towards the boundary with a less dense medium.
A. The reflected pulse in medium 1 ____will not ____ (will, will not) be inverted because _______.
B. The speed of the transmitted pulse will be ____greater than_______ (greater than, less than, the same as) the speed of the incident
pulse.
C. The speed of the reflected pulse will be _less than _____________ (greater than, less than, the same as) the speed of the incident
pulse.
D. The wavelength of the transmitted pulse will be ____greater than_______ (greater than, less than, the same as) the wavelength of
the incident pulse.
E. The frequency of the transmitted pulse will be ______same_____ (greater than, less than, the same as) the frequency of the incident
pulse.
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Case 2: A pulse in a less dense medium is traveling towards the boundary with a more dense medium.
A. The reflected pulse in medium 2 ___will _____ (will, will not) be inverted because _____________.
B. The speed of the transmitted pulse will be __less than_________ (greater than, less than, the same as) the speed of the incident
pulse.
C. The speed of the reflected pulse will be ____greater than__________ (greater than, less than, the same as) the speed of the
incident pulse.
D. The wavelength of the transmitted pulse will be ___less than________ (greater than, less than, the same as) the wavelength of the
incident pulse.
E. The frequency of the transmitted pulse will be ____the same as_______ (greater than, less than, the same as) the frequency of the
incident pulse.
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A plane wave approaches and passes through the boundary between two media. The speed of the
wave in medium 1 is greater than that in medium 2. Which one of the following diagrams
correctly shows the wave fronts? A
A.
B.
Medium 1
Medium 1
Medium 2
Medium 2
C.
D.
Medium 1
Medium 2
Medium 1
Medium 2
This question is about waves and wave properties.
(a)
By making reference to waves, distinguish between a ray and a wave front.
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(3)
The diagram below shows three wave fronts incident on a boundary between medium I and
medium R. Wave front CD is shown crossing the boundary. Wave front EF is incomplete.
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A
C
E
F
medium I
medium R
B
(b)
D
(i)
On the diagram above, draw a line to complete the wave front EF.
(ii)
Explain in which medium, I or R, the wave has the higher speed.
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...........................................................................................................................
...........................................................................................................................
(a)
ray: direction in which wave (energy) is travelling;
wavefront: line joining (neighbouring) points that have the same phase /
displacement /
Or suitable reference to Huygen’s principle;
ray is normal to a wavefront;
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(b)
(i)
wavefront parallel to D;
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(ii)
frequency is constant;
since v = f λ, v  λ;
wavelength larger in medium I, hence higher speed in medium I;
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Allow solution based on angles marked on diagram or speed
of wavefronts.
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(iii)
(c)
(i)
(ii)
(iii)
(iv)
ratio =
vI I
(or based on Snell’s law);

vR R
3.0
= 1.5 = 2.0 allow  0.5;
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velocity / displacement / direction in (+) and (–) directions;
idea of periodicity;
2
period = 3.0 ms;
1
frequency =
= 330 Hz;
T
Accept any one of the following.
at time t = 0, 1.5 ms, 3.0 ms, 4.5 ms, etc;
2
1
area of half-loop = 140  10 squares
/ mean v = 4.0 m s–1 accept  0.2;
= 140 × 0.4 × 0.1 × 10–3 / 4.0 × 1.5 × 10–3;
= 5.6 × 10–3 m
/ 6.0 × 10–3 m;
2
Award [1] for area of triangle.
(v)
(twice) the amplitude;
1
Allow distance moved in 1.5 m s.
[17]
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2. Index of Refraction and Snell’s Law
Do 23 – 28 packet examples
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7
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Tsokos p. 233 : Q2,
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p. 237: 8, 9
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3. Diffraction pp. 238 – 240 Tsokos
Tsokos p242 1- 3
.
.
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Sound waves diffract much more than light waves and can go around corners
much better. Use a mirror for reflection.
More Examples:
1. A person is walking along one side of a building and a car is driving along another side of
the building. B
The person can hear the car approach but cannot see it. This is explained by the fact that
sound waves
A.
travel more slowly than light waves.
B.
are diffracted more at the corner of the building than light waves.
C.
are refracted more at the corner of the building than light waves.
D.
are longitudinal waves.
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2. Which diagram best shows diffraction of plane wave fronts at a single slit? A
A.
B.
C.
D.
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3. Plane wave fronts are incident on a barrier as shown below.
barrier
Which of the following best shows the shape of the wave fronts on the other side of the
barrier? A
A.
B.
C.
D.
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4. Interference
http://www.physicsclassroom.com/Class/waves/ Read Lesson 3c and answer the following
question:
1.Define wave interference.
Wave interference is the phenomenon that occurs when two waves meet while traveling along the same
medium. The interference of waves causes the medium to take on a shape that results from the net effect of
the two individual waves upon the particles of the medium
2.Distinguish between constructive and destructive interference.
Constructive interference : the displacement of the two waves is in the same direction and is
additive resulting in one over all larger displacement.
Destructive interference : the displacement of the two waves is in the opposite direction and is
subtractive resulting in one over all smaller displacement or sometime zero displacement.
3.Label the following diagrams as either constructive or destructive inference:


CONSTRUCTIVE
CONSTRUCTIVE
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
DESTRUCTIVE

DESTRUCTIVE
State the Principle of Superposition.
When two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of
the displacements of the individual waves at that same location
In actuality, the task of determining the complete shape of the entire medium during interference demands
that the principle of superposition be applied for every point (or
nearly every point) along the medium.
At position A, there is no displacement for either individual wave;
thus, the resulting displacement of the medium at position will be 0
units
At position B, the smaller wave has a displacement of
approximately 1.4 units (indicated by the red dot); the larger wave
has a displacement of approximately 2 units (indicated by the blue
dot). Thus, the resulting displacement of the medium will be
approximately 3.4 units. At position C, the smaller wave has a
displacement of approximately 2 units; the larger wave has a
displacement of approximately 4 units; thus, the resulting
displacement of the medium will be approximately 6 units
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Check Your Understanding
1. Several positions along the medium are labeled with a
letter. Categorize each labeled position along the medium
as being a position where either constructive or destructive
interference occurs.
Constructive Interference: G, J, M and N
Destructive Interference: H, I, K, L, and O
2. Twin water bugs Jimminy and Johnny are both
creating a series of circular waves by jiggling their
legs in the water. The waves undergo interference
and create the pattern represented in the diagram
at the right. The thick lines in the diagram
represent wave crests and the thin lines represent
wave troughs. Several of positions in the water are
labeled with a letter. Categorize each labeled
position as being a position where either
Constructive Interference: A and B
Destructive Interference: C, D, E, and F
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TSOKOS: Read pages 240-242 and answer the following questions:
1. Outline the conditions required for constructive and destructive interference. Use the
terms ‘path difference’ and ‘phase difference’.
2. Answer problem 51 below.
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A pulse is sent down a string fixed at one end.
Which one of the following diagrams best represents the reflected pulse? C
A.
B.
C.
D.
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5. Single Slit Diffraction Tsokos pp. 261 -265 SL Text p. 96 – 97, 226 –
227
IB Example This question is about diffraction.
Plane wave fronts of monochromatic light of wavelength  are incident on a rectangular slit
of width b. After passing through the slit, the light is brought to a focus on a screen distance
D from the slit as shown below. The width of the slit is comparable to the wavelength of the
incident light and b  D. The point P on the screen is opposite the centre of the slit.
b
P
D
slit
screen
The sketch graph below shows that the variation with angle  of the intensity of the light on
the screen.
intensity
 
Explain qualitatively, this intensity distribution.:
Question is asking about bright spots ( maxima) and dark spots ( minima). Bright spots are due
to a path difference of one or multiple of one wavelength resulting in constructive interference..
Minima are dark spots due to a path difference of ½ wavelength and multiples of ½
wavelength) resulting in destructive interference
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Example 1 : Light of wavelength 500 nm ( 1nm = 10-9 m) is diffracted by a single slit
0.05 mm wide. Find the angular position of the first minimum.
θ = λ = 500 x 10-9m
b
0.00005 m
= 0.01 rad
note units: rad
Example 2 : When light with a wavelength of 440 nm is diffracted through a single slit,
the angular position of the first minimum is found to be 0.02 rad. Calculate the width of
the slit.
Rad vs. degrees 1800 = π rad
Converting rads to degrees : 1 rad = 3600
2π
Example 3 : Convert 0.5 rad to degrees
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Example 4 :
A single slit width 0.0015 mm is illuminated with light of wavelength 500.0 nm. Find the
angular width of the central maximum in degrees ( not rads).
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Young’s Double Slit Experiment– See video and answer questions:
1. Drawing
2. Why do you not get only two bright spots? Because of diffraction. Waves do not
travel straight through the slits, they spread or diffract producing constructive and
destructive patterns and a series of dark and bright spots.
Similar to single slit diffraction pattern
intensity
 
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3. Briefly explain the path length difference and constructive and destructive
interference as related to bright and dark spots:
If the path length difference Δ x = 1 λ you get constructive interference and bright spots.
If Δ x = 1/2 λ you get destructive interference and bright spots .
4. Explain the following drawing: Central Maximum no path difference. Δ x, -x2 =0
Central Maximum
X1 represents the distance that the wave follows from the top slit that is equal to X2
which represents the distance that the wave is following from the bottom slit. This
proves that the path difference is zero so the Δ x = 0 at the central maximum .
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5. Constructive interference at multiples of path length difference of one λ going up
away form the central maximum.
Note NOT the distance between the points on the wall. But the difference between the
path of the waves
But the difference between the path of the waves:
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6. Finally get distribution of dark and bright spots, constructive interference = path
difference multiples of 1 λ and destructive interference = path difference of 1/2 λ
8. Interference – Young’s Double Slit : Formulas Tsokos pp. 624-627
Example:
In a Young’s two slit experiment, a source of light of unknown wavelength is used to
illuminate two very narrow slits a distance of 0.15 mm apart. On a screen at a distance
of 1.30 m from the slits , bright spots are observed separated by a distance of 4.95 mm.
What is the wavelength of light being used?
S = λ D in data booklet
d
λ = Sd = ( 0.00495 m) ( 0.00015m) = 5.71 x 10-7 m = 571 nm
D
(1.3m)
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9. Polarization Tsokos pp. 271 – 272
Example
This question is about polarization.
(a)
State what is meant by polarized light.
When a lens or piece of glass is cut that allow waves of a certain orientation to pass through.
For example, plane polarization may only let waves of a vertical or horizontal
orientation to pass through.
(b) On the axes below, sketch a graph to show the variation with angle  of the
intensity of the transmitted light.
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Tsokos p. 278 : 1-3, 13
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Brewster's Law
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Tsokos p. 275 Q2
NOTE θB
tanθB = 1.33  tanθp = 1.33
1.00
= θp
solve for θp
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