1. R1R1 R2R2 Synchronous (in phase) waves from two point sources travel different path lengths to reach point A. A Point A will experience complete destructive interference if, for some integer m, the path difference  = R 1 -R 2 is exactly equal to 1. m 3. ( m+ 1 / 4 ) 4. 0

2. Double-Slit Interference Path difference  between waves determines phase difference m is an integer: m = 0, ± 1, ± 2,...  d L y  r1r1 r2r2  = d sin  For Destructive Interference  = 1 / 2, 3 / 2, 5 / 2, 7 / 2, … = ( m + 1 / 2 ) d sin  = ( m + 1 / 2 ) For Constructive Interference  = 1, 2, 3, 4, … = m d sin  = m If  is small (r 1, r 2 >d) then :

3. Exposed to Neon laser light passing uninterrupted through a narrow pair of slits, point P is the location of a bright fringe in the resulting interference pattern. P If a thin plate of clear crown glass held normal to the path to P covered one of the slits, the point P would (1) still be a point of constructive interference. (2) be a node (dark fringe) of destructive interference. (3) have a phase difference between the two slits that depended on the thickness of the plate.

4. Exposed to Neon laser light passing uninterrupted through a narrow pair of slits, point P is the location of a bright fringe in the resulting interference pattern. P If a thin sheet of clear crown glass precision ground exactly to a thickness equal to an odd number of wavelengths N is held normal to the path to P covered one of the slits, the point P would (1) still be a point of constructive interference. (2) become a node (dark fringe) of destructive interference. (3) have a phase difference between the two slits that depended on the number N. n glass =1.5

5. Answers to multiple choice conceptual questions. 3. have a phase difference that depends on the plate’s thickness. 2. become a node (dark fringe) of destructive interference. Within the glass, wavelengths of light are shortened: n = /n. So the introduction of the glass plate changes the total number of waves in the path from the lower slit to P. Exactly how many wavelengths (and whether it is even exactly a whole number of Wavelengths) depends on the glass’ thickness. With no glass plate, the air space where the (thickness t) glass Would have been carries N=t/ wavelengths of laser light. When in place the glass’ thickness is filled by N glass = t/ n = n g (t/ ) waves. That’s n g  N = 1.5N waves compared to N. That makes point P effectively 0.5N wavelengths further from the lower slit when the glass is in place, which is an added 0.5N phase difference. 2. (m+ ½)