University of Kentucky

Department of Physics and Astronomy

PHY 308 Principles of Optics

Spring 1997

Test 2. March 12, 1997 (Wednesday)

Time allowed: 1:00 p.m. to 1:50 p.m.

Answer all four questions (25 points for each question).

Write down and show your work clearly.

  1. A comet subtends an angle of 0.2o at the objective lens of a terrestrial telescope. The focal lengths of the object and ocular lenses are 25cm and 10cm, respectively. Find the length of the image of the comet viewed through the telescope at a point of 20cm in front of the ocular lens.
    Solution:


2.
a. (12 points)
A hyperopic (i.e. farsighted) person has to wear lenses of focal length 33.33 cm to correct the vision. What is the near point of that person?

Solution:



b. (13 points)
The same person is trying to read newspaper (without wearing correction glasses) with a magnifying glass of focal length 5cm. If the newspaper is placed 25cm in front of the eyes, what is the maximum distance between the magnifying glass and the newspaper?

Solution:


3. Calculate Total = 1 + 2 in each of the following cases. Give name for each phenomenon.

a. (8 points)
1 = 4 cos (2x - 3t)
2 = 4 cos (2x - 3t + 60o)
Solution:


Superposition of coherent waves.

b. (7 points)

1 = 4 sin (5x - 7t)
2 = 4 sin (6x - 6t)

Solution:

Beating.

c. (7 points)

1 = 4 cos (x - t)
2 = 4 cos (x + t)

Solution:



4.

a. (10 points)
Fourier transform the voltage V(t) defined in the figure into A(). If V(t) is in volts, what is the unit for A()?


Solution:





b. (10 points)
Consider a piece of electronic equipment with the following properties:

If a voltage of V0e-it is applied to the input, then the output will be -iV0e-it .

The voltage V(t) in part (a) is now connected to the input of this equipment, what will be the output voltage as a function of time? Sketch the output voltage.
Solution:






c. (5 points)
How would you like to call the equipment (choose one):
A. Frequency generator
B. Chopper
C. Integrator
D. Differentiator
E. Comparator

Give reasons:

D. Differentiator. As can be seen from the drawings in part (b), V output is simply the derivative of V input. This is obviously the case because the equipment is differentiating every harmonic in the input.