Physics 375: OPTICSProblem Set 8

Due: 12 April 2017

Problem 1. A coin of diameter Dc is 300 cm in front of a wall (theplane of the coin is parallel to that of the wall). A circular flat mirrorof diameter Dm hangs on the wall. If a person stands 900 cm from thewall, show that the smallest diameter mirror in which the observercan just see the reflected image of the coin (i.e. the image of the coinjust fills the mirror) is given by

Dm =34

Dc

Problem 2. An object 2cm high is positioned 5cm to the right of apositive thin lens with a focal length of 10 cm. Descibe the resultingimage completely, using:

(a) the Gaussian equations, and

(b) the Newtonian equations.

Figure 1: The lens for Problem 3.

Problem 3. A homemade telephoto lens (See Figure 1) consists of twospherical mirrors. The radius of curvature is 2.0 m for the primary(the larger mirror) and 60 cm for the secondary. How far from thesecondary mirror should the film plane be located if the object is astar? What is the effective focal length of the system?

Problem 4. A homemade telephoto lens (See Figure 1) consists of twospherical mirrors. The radius of curvature is 2.0 m for the primary(the larger mirror) and 60 cm for the secondary. How far from thesecondary mirror should the film plane be located if the object is astar? What is the effective focal length of the system?

Problem 5. Determine the optical path difference for the two waves A andB, both having vacuum wavelengths of 500 nm, and depicted in the figurebelow. The glass (n=1.52) tank is filled with water (n=1.33). If the wavesstart in phase and all the numbers given above are exact, find their relativephase difference at the finishing line.