1.3 refraction

Chapter 1:WavesChapter 1:Waves
1.3 Analysing Refraction ofWaves

1.31.3 Analysing Refraction of WavesAnalysing Refraction of Waves
 Any type of wave can be refracted, which means a
change of direction. Refraction occurs when the speed
of a wave changes, as it moves from one medium to
another. We shall look at the refraction of water
waves, light waves and sound waves.

Refraction of Plane Water WavesRefraction of Plane Water Waves
 1 Water waves undergo refraction (bending) when
they are slow down. Refraction is accompanied by a
change in speed and wavelength of the waves.

 2 Water waves travel faster (with higher velocity, v)
on the surface of deep water than they do on shallow
water. Thus, if water waves are passing from deep
water into shallow water, they will slow down. This
decrease in speed will also be accompanied by a
decrease in wavelength. The change in speed of the
wave causes refraction.
 Figure 1.31

 3 After refraction, the wave has the same
frequency, but a different speed, wavelength and
direction.

 4 When a water wave transmitted from deer water
into shallow water, the wave is refracted towards the
normal.

 Conversely, the wave is refracted away from the
normal when the water wave transmitted from shallow
water into deep water. The effects of refraction of
water waves are shown in Figures 1.32 (a) and (b).

 Experiment 1.4: To investigate the
refraction of water waves
 What are the effects on the direction
of propagation of a water wave passing
over Perspex plates of different
shapes?

 Hypothesis
 Refraction occurs and the direction of propagation is
influenced by the shapes of the Perspex plates.

 Variables:
 (a) Manipulated : Shapes of Perspex plates
 (b)Responding : Wavelength and
direction of propagation of the water
wave
 (c) Fixed : Frequency

 Apparatus/Materials
 Ripple tank, wooden bar, perspex plates of different
shapes, mechanical stroboscope and white paper.

 Procedure
 1 A ripple tank is set up as shown in Figure 1.30.

 Procedure
 2 The tank is filled with water and the legs of the
tank are adjusted until the depth of the water in the
tank is uniform.

 Procedure
 3 A Perspex plate in the shape of a trapezium, as
shown in Figure 1.31, is immersed in the centre of the
tank to create an area of shallow water in the tank.

 Procedure
 4 The dipper with the wooden bar attached is
switched on to produce plane waves.

 Procedure
 5 The directions of the water waves in the areas of
deep and shallow water are observed with a
stroboscope.

 Procedure
 6 Steps 3 to 5 are repeated with the orientation of
the trapezium plate changed so that the wave is
incident at an acute angle on a side of the plate as
shown in Figure 1.32.

 Procedure
 7 Steps 3 to 5 are repeated using Perspex plates in
the shapes of a triangle, convex lens and concave lens.
Position Observation
(a) Trapezium Perspex
plate with the vertical
side of the plate
facing the incident
wave.

 Procedure
(b) Trapezium Perspex
plate with the slant side
of the plate facing the
incident wave.

 Procedure
(c) Triangular Perspex plate

 Procedure
(d) Perspex plate in the
shape of a convex lens

 Procedure
(e) Perspex plate in the
shape of a concave lens

 Discussion
 1 Refraction occurs when a water wave passes from
one area to another area with a different depth of
water.

 Discussion
 2 If the wave strikes the perspex plate at an angle of
incidence of 0°, the direction of propagation of the
wave remains unchanged. The water wave is not
refracted, i.e. the angle of refraction is zero.

 Discussion
 3 If the wave strikes the Perspex plate at a certain
angle of incidence, the water wave is refracted.

 Discussion
 4 The water wave is refracted towards the normal
the wave travels to a shallower area, and vice versa.

 Conclusion
 The direction of propagation of a wave changes if the
angle of incidence of the wave is not zero. The shape,
of the refracted wave depends on the shape of the area
of shallow water over which the wave is passing.

 Example 7:
 Figure 1.35 shows water ripples in two areas of water
with different depths. The observation is made with a
stroboscope with 3 slits. The frequency of the
stroboscope is 4 rotations per second

 Calculate
 (a) the frequency of the dipper,

Solution
 (a) Frequency of dipper
 = Number of slits x Frequency of stroboscope
 = n x p
 = 3 x 4
 = 12Hz


 Calculate
 (b) the wavelength in the deep area and in the shallow
area,

 Solution
 (b) Area of deep water:
 Wavelength ,
 Area of shallow water:
 Wavelength
cm2
3
6
1 ==λ
cm8.0
3
4.2
2 ==λ

 Calculate
 (c) the speeds of the waves in the two areas.

 Solution
 (c) Area of deep water:
 Speed
 Area of shallow water:
 Speed
 = 9.6 cm s-1
1
11 24212 −
=×== cmsfv λ
1
22 8.012 −
×== cmsfv λ

 Example 8
 A plane wave has a wavelength of 2 cm and a velocity of
8 cm s-1
as it moves over the surface of shallow water.
When the plane wave moves into an area of greater
depth, its velocity becomes 12 cm s-1
. What is
 (a) the wavelength
 (b) the frequency of the wave in the area of greater
depth?

 Solution
 (a) Area of shallow water:
 v1=8 cm s-1
and λ1=2cm
 Area of deeper water:
 v2=12 cm s-1
and λ2=?
 For refraction, frequency, f =
remains the same.
 Substituting in the relationship:

λ
v

 Example 8
 A plane wave has a wavelength of 2 cm and a velocity of
8 cm s-1
as it moves over the surface of shallow water.
When the plane wave moves into an area of greater
depth, its velocity becomes 12 cm s-1
. What is
 (b) the frequency of the wave in the area of greater
depth?

 Solution
 (b) Frequency of wave, f = = 4 Hz

 The frequency of the wave is the same in all the areas.
λ
v

Refraction of lightRefraction of light
 1 A swimming pool seems much shallower than it
actually is; a spoon appears bent when part of it is in
water and a boy's legs look shorter when immersed in a
pool. All these effects are due to the refraction of
light.

 2 Figure 1.37 shows that a light ray is bent or
refracted when passing from air to the glass.

 3 When a ray propagates from one medium to an
optically denser medium, the ray refracts towards
the normal. Conversely, a ray propagating from one
medium to an optically less dense medium is refracted
away from the normal.

 4 The speed of the light decreases as it propagates in
the glass block, causing it to alter the direction of
propagation. Since the incidence ray and the refracted
ray are from the same source (ray box), the frequency
remain the same. Hence, the wavelength of the ray in
the glass is shorter than the ray in the air.

Refraction of Sound WavesRefraction of Sound Waves
 1 The sound of a moving train at a distance is clearer
at night than that in the day time. This is due to the
effects of the refraction of sound waves.

 2 At night-time, the layers of air close to the ground
are cooler than the layers further from the ground.

 3 Sound travels at a slower speed in cold air. As a
result, the sound waves are refracted in front path of a
curve (due to total internal reflection) towards the
ground instead of disappearing into the upper layers of
the air.

 Experiment 1.5 To investigate the refraction of sound waves
 What happens to a sound wave as it passes through a
balloon filled with carbon dioxide?

 Hypothesis
 A sound wave of greater amplitude is produced after it
passes through the balloon filled with carbon dioxide.

 Variables
 (a) Manipulated : Balloon filled with carbon dioxide
 (b) Responding : Amplitude of the sound wave
displayed on the screen of the cathode-ray oscilloscope
 (c) Fixed : Frequency of the sound wave

 Apparatus
 Audio signal generator, loudspeaker, balloon fillet with
carbon dioxide, microphone and cathode-ray
oscilloscope.

Procedure
1 The apparatus is set up as shown in Figure
1.39.
Figure 1.39

Procedure
2 The experiment is started without the balloon.

Procedure
3 The audio signal generator and the cathode-ray
oscilloscope are switched on. The wave form
displayed on the screen of the oscilloscope is
observed and drawn.

Procedure
4 A balloon filled with carbon dioxide is placed
between the audio signal generator and the
oscilloscope.
5 The wave form displayed on the screen is
observed and drawn.

 Results

Results
 The wave form displayed on the oscilloscope shows
that the amplitude is larger when the balloon is placed
between the audio signal generator and the
oscilloscope. The larger amplitude indicates that a
louder sound is received by the microphone.

 Discussion
 A sound wave is refracted towards the normal when
the wave passes from the air to the carbon dioxide in
the balloon. This is because carbon dioxide is denser
than air and the speed of sound in carbon dioxide is
reduced.

 Discussion
 When the sound wave emerges from the balloon, the
wave is refracted away from the normal. The balloon
acts as a biconvex lens which converge the sound
waves to the microphone.

 Conclusion
 Sound waves are refracted when they travel from one
medium to another of different density. The sound
waves are refracted away from the normal after passing
through the balloon filled with carbon dioxide. The
result is a sound wave with larger amplitude.
 The hypothesis is valid.

1.3 refraction

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