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1 A beam of vertically polarised monochromatic light is incident on a polarising filter, as shown in

Fig. 5.1.

polarising filter

vertically polarised transmitted light beam

incident light beam

direction of
transmission axis

Fig. 5.1

The transmission axis of the filter is initially vertical and the transmitted light beam has the same
intensity as the incident light beam.

The filter may be rotated about the direction of the light beam to change the angle of the
transmission axis to the vertical.

(a) State one angle of the transmission axis to the vertical that results in no transmitted light
beam.

angle = ......................................................... ° [1]

(b) The filter is now positioned with its transmission axis at angle θ to the vertical, as shown in
Fig. 5.2.

θ
vertically polarised transmitted light beam
incident light beam

transmission axis
at angle θ to the vertical

Fig. 5.2

intensity of transmitted light

The ratio is equal to 0.75.
intensity of incident light

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(i) Calculate angle θ.

θ = ......................................................... ° [2]

(ii) Calculate the ratio

amplitude of transmitted light

.
amplitude of incident light

ratio = ........................................................... [2]

 [Total: 5]

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5 2 (a) Two progressive sound waves meet to form a stationary wave. The two waves have the
same amplitude, wavelength, frequency and speed.

State the other condition that must be fulfilled by the two waves in order for them to produce
the stationary wave.

............................................................................................................................................. [1]

(b) A stationary wave is formed on a string that is stretched between two fixed points A and B.
Fig. 5.1 shows the string at time t = 0 when each point is at its maximum displacement.

A B

Fig. 5.1

Distance AB is 0.80 m. The period of the stationary wave is 0.016 s.

(i) On Fig. 5.1, sketch a solid line to show the position of the string:

● at time t = 0.004 s (label this line P)

● at time t = 0.024 s (label this line Q).

[2]

(ii) Determine the speed of a progressive wave along the string.

speed = ................................................ m s–1 [3]

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(c) A beam of vertically polarised light of intensity I0 is incident normally on a polarising filter that
has its transmission axis at 30° to the vertical, as shown in Fig. 5.2.

vertically polarised
incident light 30° transmitted transmitted
beam, beam, beam,
intensity I0 intensity I1 intensity I2

polarising filter with second polarising filter

transmission axis at with transmission axis at
30° to the vertical 90° to the vertical

Fig. 5.2

The transmitted light from the first polarising filter has intensity I1. This light is then incident
normally on a second polarising filter that has its transmission axis at 90° to the vertical. The
transmitted light from the second filter has intensity I2.

Calculate:
I1
(i) the ratio
I0

I1
= ......................................................... [2]
I0
I2
(ii) the ratio .
I0

I2
= ......................................................... [2]
I0
[Total: 10]

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3
4 (a) Polarisation is a phenomenon associated with light waves but not with sound waves.

(i) State the meaning of polarisation.

...........................................................................................................................................

...........................................................................................................................................

..................................................................................................................................... [1]

(ii) State why light waves can be plane polarised but sound waves cannot.

...........................................................................................................................................

...........................................................................................................................................

..................................................................................................................................... [1]

(b) Two polarising filters A and B are positioned so that their planes are parallel to each other and
perpendicular to a central axis line XY, as shown in Fig. 4.1.

filter filter
A B
direction of
rotation

I0
X Y
unpolarised
light

vertical horizontal
transmission axis transmission axis

Fig. 4.1

The transmission axis of filter A is vertical and the transmission axis of filter B is horizontal.

Unpolarised light of a single frequency is directed along the line XY from a source positioned
at X. The light emerging from filter A is vertically plane polarised and has intensity I0.

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Filter B is rotated from its starting position about the line XY, as shown in Fig. 4.1.
1
After rotation, the intensity of the light emerging from filter B is I0.
4
Calculate the angle of rotation of filter B from its starting position.

angle of rotation = ....................................................... ° [3]

(c) A microwave of intensity I0 and amplitude A0 meets another microwave of the same frequency
1
and of intensity I0 travelling in the opposite direction. Both microwaves are vertically plane
4
polarised and superpose where they meet.

(i) Explain, without calculation, why these two waves cannot form a stationary wave with
zero amplitude at its nodes.

...........................................................................................................................................

...........................................................................................................................................

..................................................................................................................................... [2]

(ii) Determine, in terms of A0, the maximum amplitude of the wave formed.

maximum amplitude = .................................................... A0 [3]

[Total: 10]

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