# homework assignment

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```					           Year 12 Net-Based, Animated-Homework Waves
Refraction, Diffraction and Interference
sin 1 v1 λ1 n2                             1
n1 sin 1  n2 sin  2         n2                       v =f λ       f 
sin  2 v2 λ 2 n1
1
T
index of refractions: air = 1.00, water = 1.33, ethanol = 1.36, diamond = 2.42

Question #3: Fishes + Earth + Deep & Shallow)
Daria has a special, thought to be extinct, golden guppy that can
shoot lasers from its eyes (like the top animation).
a) Calculate the span of degrees (from the normal) that the fish
can target its prey above the water. (This can also be called
the critical angle.)
b) If the fish shoots its laser at an angle of 35 degrees to the
surface, determine what will happen to the laser light with
calculations and a labelled diagram.
Dingo's cousin, Dungbat is a geophysicist. Dungbat tells Dingo and
Daria about the different parts of the earth and the pressure p-wave
made by earthquakes (like the second animation).
c) Explain what will happen to the p-wave as it hits the barrier
between the mantle and the liquid core. Include details.
d) What was the importance of people figuring this out?

Dingo and Daria decide to go surfing in a man-made wave-pool
that has 2 distinct depths of water like 3rd animation. The
incident angle is 49° and the refracted angle is 33°. The incident
wave also has a wavelength of 5.5m and a speed of 2.9m/s.
e) Which region is the deep and which region is the shallow
water?
remains constant? (remember: there are 4 things you can

g) Calculate (i) the refractive index for this boundary, (ii) the new
wavelength and (iii) velocity.
h) If the waves were reversed (to travel the other way) but the incident angle was changed to
39° and the initial wavelength is now 3.1m with a speed to 3.9ms-1, (i) SHOW that the new
refractive index for this direction ≈ 0.72, then calculate (ii) the new refracted angle, (iii) the
new wavelength and (iv) the new velocity.

Question #4: Diffraction definition and rules
Dingo learns a new term: "diffraction". Daria doesn't understand what he's on about. You can
a) Explain the similarities and difference between the terms "refraction" and "diffraction".
b) If plane waves hit a gap in a wall, how will Dingo and Daria predict if diffraction happens?
Be specific and describe when diffraction happens and when it doesn't.
c) If plane waves hit a barrier, how will Dingo and Daria now predict if diffraction happens?
Again, be specific and describe both possibilities.
TRY IT (Bauer)

Question #5: More Diffraction (gap, hills and                                          light)
Dingo sets up his own wave tank with a variable gap like
the 1st animation. With the gap small he sees
diffraction of the plane waves.
a) Explain what he will see as he progressively makes
the gap larger, and why.
Dingo realizes that TV and radio both use waves to
transmit their signals. But his surfing shack is
behind a tall hill like the 2nd animation. Daria tells
him that TV stations use higher frequency than radio
stations.
b) Which of the two types of waves, TV or radio, will
not diffract over the hill to reach Dingo's surfing
shack? Why?
c) What will have to happen for his surfing shack to receive this signal without Dingo moving
or putting up an epically tall aerial?
d) Of the two types of radio stations, AM and FM, which will diffract more? Why? You might
need to look at your radio to see the units for each type of station.

Daria figures that since light is a wave it should diffract just like
water waves. She sets up a changeable laser to shoot at a small
hole of changeable width like the bottom animation. She is
surprised to see fringes of colour on her screen! Fringes are bright,
fuzzy spots of light.
d) Explain what is happening as the light passes through the gap.
e) If she changes the light to a smaller wavelength, (i) what colour
is she shifting towards, and (ii) how will the fringe pattern
change?

Question #6: Ropes and Strings
Dingo and Daria go outside and wind up playing with some ropes. Daria ties one rope to a
tree and flicks a pulse down the rope towards the tree. Dingo ties his rope to a flagpole loop
so that it is free to move. Dingo flicks a pulse down his rope as well. The top animations can
(a) Draw the before and after diagrams for each rope, Daria's fixed and Dingo's free. Label
the velocity and width of the pulse remembering relative size in your 4 diagrams.
Daria's rope is thinner than Dingo's. They decide to tie them together. First Daria flicks a
pulse down her rope towards Dingo.
(b) Draw 2 diagrams (before the pulse enters Dingo's rope and after) with relative sizes and
labels for velocity and width of pulses.

After the ropes settle, Dingo flicks a pulse on his rope towards Daria.
(c) Again, draw 2 diagrams (before the pulse enters Daria's rope and after) with relative sizes
and labels for velocity and width of pulses.
Dingo decides to connect his rope to the tree and instead of sending a single pulse, he
vibrates the end vigorously like the second animation above. While he does this Daria stands

off to the side so she can see the entire length of the rope.

TRY IT (Surandranath, Waves, Pulses)

TRY IT (Fendt)

TRY IT (CKNG)
(d) Explain what will happen if he continues to vibrate his end while the pulses are reflected.
Make a labelled diagram for what Daria will see. What is this phenomenon called?
Daria connects one end of a piece of string to a stand and the other to an oscillator of variable
frequency, like the 3rd animation above. She starts at 20Hz and slowly increases the
frequency to 30Hz. At 25Hz she sees the 1st possible standing wave.
(e) Draw the diagram for this standing wave and label its parts.
(f) If she were to triple the frequency, (i) draw the diagram for the new standing wave, (ii) label
its parts and (iii) explain how these parts are created.

Question #7: Water + Sound + Lasers
Dingo and Daria now set up a water tank with two pegs that bounce in and out of the water at
the same frequency (like the top animation).
(a) Draw a diagram for the location of the antinodes and nodes as seen from above the water
tank.
(b) Explain what they will see on the surface of the water once the waves reach across the
entire tank. Be specific and explain why these things are happening.
(c) If they were to decrease the frequency of the two pegs, would the pattern of antinodes
and nodes change. If so, how?
Daria's cousin, Desdimona, is a sound engineer and sets up two speakers for Dingo and
Daria that produce the same frequency (like the 2nd animation). Dingo's dad, Dilburt, stands
exactly in between the two speakers but 4 metres away.
(d) (i) Draw a diagram for the two speakers and the locations of the antinodes and nodes.
(ii) Specifically explain why these occur at these locations. (The answer to #7a may
(e) Dilburt decides to walk parallel to the speakers (upwards in the picture shown). Explain

what he will hear and explain why.
TRY IT (Uni of Salford)

TRY IT (PHET, waves)

(f) Daria then changes the sound the speakers produce to a higher pitch. Explain how the
situation is now changed and why.
Finally, Dingo's older sister, Dee, sets up her laser from her high-tech laboratory. The laser is
shot through two movable holes in a solid wall. On a screen behind the wall fringes appear.
(g) Explain how the fringes appear by using the TWO physics phenomena involved.
(h) Dingo adjusts the holes so they are closer together. How is the pattern of fringes
affected?
(i) If Daria could change the colour of the laser to be red (instead of green that was originally
used), how would the pattern of fringes be affected?                            Check your
work
Question #1. Refraction Investigation
Dingo and Daria are surfers from the gold coast. In their physics class they are learning
block and a ray box to experiment with (like the 2 animations to the right). They first trace a
ray diagram like the left animation shows.

(a) What does the term "refraction" mean exactly?
TRY IT          TRY IT
(b) What exactly does the "n1" and "n2" mean in the diagram and in Snell's Law?
(c) What is the dotted line in each diagram called?
(d) Using Snell's Law, calculate the index of refraction of their glass block, assuming they've
measured the incident and refracted angle correctly.
(e) They then change their setup to look at light trying to exit the glass (like the 2nd
animation). Explain how the angles change as light enters and exits glass from air. Also
explain why.
(f) What 2 special things can happen as they look at the glass-air boundary. Draw 2 labelled
Dingo is told to make 12 sets of measurements and then graph sine of incident angle vs sine
of refracted angle. His values are: 60, 27; 56, 25; 52, 24; 47, 22; 41, 20; 35, 17;
31, 15, 25, 13; 19, 10; 15, 8; 9, 5. (each point is incident angle, refracted angle).
(g) (i) Graph the sine of the incident angle vs the sine of the refracted angle and (ii) draw a
line of best fit, then (iii) find the gradient and (iv) write the equation of the line.
(h) (i) What is the meaning of the gradient of your line and (ii) why is this a better
Question #2: Dingo's gemstones & Alexia's prism
Dingo is from the outback where gemstones are mined. He takes one of his diamonds and
places it in water, then shines a light ray at the flat edge. The top animation to the right can
be adjusted to Dingo's experiment. Very carefully, Daria measures the incident angle in the
water at 31.6°.
(a) Calculate the refracted angle inside the diamond.
(b) Explain why the light ray changes direction.
Daria sets up another experiment with a light ray shining through stone salt towards ethanol.
She carefully measures the incident angle at 60.1 and the refracted angle at 79.0.
(c) Calculate the index of refraction for the stone salt.
(d) Calculate the critical angle for this situation.
Daria then grabs her set of crystals that she made in her glass-blowing class and sets up a

light ray in air to strike different glasses (like the 2nd animation).
TRY IT (Fendt)

TRY IT (Harrison)
TRY IT (CKNG)
(e) Will the light ray always (i) enter any of her glass block from the air, and (ii) enter the air
from any of her glass blocks?
(f) Calculate the critical angle for one of Daria's glass blocks with an index of refraction of
1.25.
(g) Dingo thinks that if Daria replaces her 1.25 index glass block with one that has an index
30% larger, then the new critical angle will be 30% smaller. Is he right? Use Snell's law
to calculate the new critical angle and draw 2 labelled diagrams, one for the 1.25 index
block and one for the 30% larger index block.
(h) Dingo then grabs one of Daria's glass prisms (like the 3rd animation) that has 60.0
degrees at each corner and an index of 1.50. He sets up a ray box so that the light ray is
parallel to the bottom of the prism. (i) Calculate the first refracted angle inside the prism,
then (ii) the incident angle as the ray hits the other side of the prism, then (iii) the 2nd
refracted angle as the light ray exits the prism.
(i) Daria replaces the 1st prism with another one of identical shape but a higher index. This
time the 1st refracted angle is measured at 17.1. (i) Calculate the new prism's refractive
index and (ii) SHOW that the critical angle for this prism ≈ 36.0°. (iii) Draw a ray diagram
for this situation including where the light eventually goes and labelling all the angles
involved.