Unpolarized light with an intensity of 320 W m⁻² goes through a polarizer and an analyser, originally aligned parallel.

The analyser is rotated through an angle θ = 30°. Cos 30° = $\frac{\sqrt{3}}{2}$.

What is the intensity of the light emerging from the analyser? 

A.  120 W m⁻²

B.  $80\sqrt{3}$ W m⁻²

C.  240 W m⁻²

D.  $160\sqrt{3}$ W m⁻²

A point source of light of amplitude A₀ gives rise to a particular light intensity when viewed at a distance from the source. When the amplitude is increased and the viewing distance is doubled, the light intensity is doubled. What is the new amplitude of the source? 

A. 2A₀

B. 2$\sqrt{2}$ A₀

C. 4A₀

D. 8A₀

Horizontally polarized light is incident on a pair of polarizers X and Y. The axis of polarization of X makes an angle θ with the horizontal. The axis of polarization of Y is vertical.

What is θ so that the intensity of the light transmitted through Y is a maximum?

A.  $0°$

B.  $45°$

C.  $90°$

D.  $180°$

Radio waves are emitted by a straight conducting rod antenna (aerial). The plane of polarization of these waves is parallel to the transmitting antenna.

An identical antenna is used for reception. Suggest why the receiving antenna needs to be be parallel to the transmitting antenna.

Unpolarized light of intensity I₀ is incident on the first of two polarizing sheets. Initially the planes of polarization of the sheets are perpendicular.

Which sheet must be rotated and by what angle so that light of intensity $\frac{I_0}{4}$ can emerge from the second sheet?

Calculate the wavelength measured by the observer.

Show that the intensity of solar radiation at the orbit of Mars is about 600 W m^–2.

When both loudspeakers are operating, the intensity of sound recorded at Q is $I_0$. Loudspeaker B is now disconnected. Loudspeaker A continues to emit sound with unchanged amplitude and frequency. The intensity of sound recorded at Q changes to $I_{\mathrm{A}}$.

Estimate $\frac{I_{\mathrm{A}}}{I_0}$.

Unpolarized light of intensity $I_1$ is incident on a polarizer. The light that passes through this polarizer then passes through a second polarizer.

The second polarizer can be rotated to vary the intensity of the emergent light. What is the maximum value of the intensity emerging from the second polarizer?

A.  $\frac{I_1}{4}$

B.  $\frac{I_1}{2}$

C.  $\frac{2I_1}{3}$

D.  $I_1$

When both loudspeakers are operating, the intensity of sound recorded at Q is $I_0$. Loudspeaker B is now disconnected. Loudspeaker A continues to emit sound with unchanged amplitude and frequency. The intensity of sound recorded at Q changes to $I_{\mathrm{A}}$.

Estimate $\frac{I_{\mathrm{A}}}{I_0}$.

Show that the intensity of solar radiation at the orbit of Mars is about 600 W m^–2.

Two wave generators, placed at position P and position Q, produce water waves with a wavelength of$4.0 \text{cm}$. Each generator, operating alone, will produce a wave oscillating with an amplitude of $3.0 \text{cm}$ at position R. PR is$42 \text{cm}$ and RQ is $60 \text{cm}$.

Both wave generators now operate together in phase. What is the amplitude of the resulting wave at R?

A.  $9 \text{cm}$

B.  $6 \text{cm}$

C.  $3 \text{cm}$

D.  zero

The microwaves emitted by the transmitter are horizontally polarized. The microwave receiver contains a polarizing filter. When the receiver is at position W it detects a maximum intensity.

The receiver is then rotated through 180° about the horizontal dotted line passing through the microwave transmitter. Sketch a graph on the axes provided to show the variation of received intensity with rotation angle.

Show that the intensity of the solar radiation at the location of Titan is 16 W m⁻²

Show that the intensity of the solar radiation at the location of Titan is 16 W m⁻².

A light source of power P is observed from a distance $d$. The power of the source is then halved.

At what distance from the source will the intensity be the same as before?

A.  $\frac{d}{\sqrt{2}}$

B.  $\frac{d}{2}$

C.  $\frac{d}{4}$

D.  $\frac{d}{8}$

A beam of unpolarized light of intensity $I_0$ is incident on a polarizing filter. The polarizing filter is rotated through an angle θ. What is the variation in the intensity $I$ of the beam with angle θ after passing through the polarizing filter?

Explain why the received intensity varies between maximum and minimum values.

B is placed at the first minimum. The frequency is then changed until the received intensity is again at a maximum.

Show that the lowest frequency at which the intensity maximum can occur is about 3 kHz.

Speed of sound = 340 m s⁻¹

B is placed at the first minimum. The frequency is then changed until the received intensity is again at a maximum.

Show that the lowest frequency at which the intensity maximum can occur is about 3 kHz.

Speed of sound = 340 m s⁻¹