| Phys 198 | May 2, 1997 |
Problem 12. Looking up the specified material in the text, it is found that the frequency of the grating formed by the intersection of two plane waves is given by
where y is the full angle between the propagation axes of the two intersecting beams. Substituting for the given numbers, the spatial frequencies of the gratings made with HeNe light (l = 0.633 mm) are:
a) Beams each at 5 degrees to the normal of the plate, so y = 10 degrees gives a grating of spatial
frequency 
b) Beams each at 60 degrees to the normal of the plate, so y = 120 degrees gives a grating of spatial
frequency 
.
Notice the very large change in grating spacing that can be obtained by changing the angle between the beams.
Problem 13. Following the procedure shown in the images and text of the problem, a curve is obtained showing that the maximum displacement occurred in the center of the disk and that the phase difference involved was 5 fringes. However, it is necessary to get the magnitude of the sensitivity vector g in order to determine the actual deformation. Since the angle between the illumination vector and the viewing direction is given as 10 degrees, and taking into account the opposite directions of the illumination and viewing vectors, g is found to have a magnitude of cos 5o + cos 5o = 1.99 or about 2. Therefore the actual out-of-plane displacement of the center of the disk is given by
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