THE UNIVERSITY OF BRITISH COLUMBIA
 
Physics 108 Assignment # 12:
 
DIFFRACTION
 
Wed. 30 Mar. - finish by Wed. 6 Apr. 2005

1. SOUND DIFFRACTION: You are standing 30 m away from a large, soundproof building, directly in front of a 1 m wide doorway, when it opens and you hear someone blowing a loud whistle at a frequency of 1320 Hz from somewhere directly behind the door, deep inside the building. How far sideways (parallel to the wall with the door in it) must you move before the sound first becomes imperceptible? [Assume that the speed of sound is 343 m/s.]

2. 10-SLIT MINI-GRATING: Consider a series of 10 equal slits, each 0.004 cm wide, arrayed in a straight line with equal spacing so that 0.22 cm separates the centres of the first and last slits. This configuration is illuminated from behind by a distant source of light of wavelength 0.546 microns [$\mu$m].
   1. How many major intensity peaks will you see in the entire pattern displayed on a wide screen 20 m away before the pattern first fades away laterally because of the diffraction from each aperture?

   2. How far apart and how wide¹ (in mm) are the principal² maxima near the centre of the screen?

   3. Sketch the intensity pattern from the central maximum out to the second diffraction minimum on one side.

3. DIFFRACTION-LIMITED VISION: In fairly bright light the pupil of your eye will contract to a diameter of about 4 mm. Under these conditions, assuming that you have "perfect" vision,
   1. how far from your eye can you hold a book and still be able to resolve two identical black dots 10 $\mu$m in diameter, separated by 100 $\mu$m, using yellow light with $\lambda = 575$ nm?

   2. Describe in detail what you would see at this distance when observing a single white dot 10 $\mu$m in diameter on a black page illuminated with white light (all wavelengths).