1. This question is about diffraction and resolution.

Two identical sources of electromagnetic radiation, S1 and S2, emit monochromatic coherent waves of wavelength 59 μm. The waves pass through a circular aperture and are incident on a screen.

S1 and S2 are at the same distance from the aperture. The diameter of the aperture is 0.18 mm.The angle between the lines joining the sources to the aperture is 0.25 rad.

(a) S1 is turned on and S2 is turned off.

(i) Show that the angle at which the first minimum of the diffraction pattern occurs is 0.40 rad.

(ii) On the axes below, sketch a graph to show how the intensity I of the radiation from S1 varies with the diffraction angle θ.

(b) S1 is turned off and S2 is turned on. On the same set of axes in (a)(ii), sketch the intensity of the light emitted by source S2 reaching the screen. 

(c) S1 and S2 are both turned on.

(i) State the Rayleigh criterion for the images of two sources to be just resolved.

(ii) State and explain whether the images of the two sources, S1 and S2, are resolved.


2. This question is about standing waves and the Doppler effect.

The horn of a train can be modeled as a pipe with one open end and one closed end. The speed of sound in air is 330ms–1.

(a) On leaving the station, the train blows its horn. Both the first harmonic (fundamental) and the next highest harmonic are produced by the horn. The difference in frequency between the harmonics emitted by the horn is measured as 820 Hz.

(i) Deduce that the length of the horn is about 0.20 m.

(ii) Show that the frequency of the first harmonic is about 410 Hz.

(b) (i) Describe what is meant by the Doppler effect.

(ii) The train approaches a stationary observer at a constant velocity of 50 ms–1 and sounds its horn at the same frequency as in (a)(ii). Calculate the frequency of the sound as measured by the observer.

3. This question is about the eye and sight.Distinguish between photopic and scotopic vision.




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