Download Classical Optics receive full credit. Good Luck.

Classical Optics (course no. 203-12181) Midterm Exam
D. Rich
08.05.13
Please answer all questions below and show all calculations in order to
receive full credit. Good Luck.
Note that the relative weights of each part are indicated below, and are based on a
total of 100 points.
1. Imagine that we have a nonabsorbing glass plate of index n and thickness y,
which stands between a source S and observer P. (20 points)
(a) If the unobstructed wave (without the plate present) is Eu = E0 exp[i(t y/c)], show that with the plate in place the observer sees the following
wave: Ep = E0 exp[ i(t - (n - 1)y/c - y/c)].
(b) Show that if either n  1 or y is very small, then
Ep  Eu + [(n - 1)y/c] Eu exp(-i/2)
2. A glass block having an index of 1.55 is covered with a layer of water of index
1.33. (a) For light traveling in the glass, what is the critical angle at the
interface? (b) Calculate Brewster’s angle and explain carefully what happens
at this angle. (c) For light with a wavelength of 500 nm in air, what are the
wavelengths and frequency of the light in both the glass block and water? (20
points)
3. Two positive lenses are to be used as a laser-beam expander. An axial 1.0 mm
diameter beam enters a short focal length positive lens, which is followed by a
somewhat longer focal length positive lens from which it emerges with a
diameter of 8.0 mm. (a) Given that the first lens has a 50 mm focal length,
determine the focal length of the second lens and the separation between the
lenses. (b) Draw a diagram that illustrates the behavior of the beam along the
optical axis of the two-lens system. (20 points)
4. Two identical converging (convex) lenses each have focal lengths of 15 cm
and are separated by a distance of 6 cm. (a) If an object of height 1 cm is
placed 10 cm in front of the first lens, find the position and height of the final
image. (b) What is the total magnification of this lens system? Is the image
erect or inverted? (20 points)
5. A homemade telephoto “lens” (see figure below) consists of two spherical
mirrors. The radius of curvature is 2.0 m for the primary (large) mirror and 60
cm for the secondary (small) mirror. (a) How far from the smaller mirror
should the film plane be located if the object is a star? (b) What is the effective
focal length of the system? (20 points)