AST 307 · Introductory Astronomy Fall 2003

AST 307
Problem Set #4
Due Friday October 3

1. Assume you have bought an (expensive) amateur telescope with a primary lens of 10-inch diameter and 40-inch focal length, and an eyepiece lens of 1-inch diameter and 1-inch focal length.
a) What is its magnification?
b) What is its resolution in arcseconds, as limited by diffraction?
c) How does its light gathering power compare to that of the naked eye?
(You'll have to come up with some way to measure the diameter of your pupil.)
d) Why was this refracting telescope so much more expensive than the 10-inch reflecting telescope the store was selling? (Make a reasonable guess.)
e) Does this telescope have any advantages over the cheaper reflector?

2. A policeman used his radar gun to catch you going 35 mph in a 20 mph school zone. His radar gun emitted radio waves with a wavelength of 3 cm. When those radio waves bounced off of your car, the Doppler effect caused them to change wavelength and frequency.
a) What was the frequency of the radio waves emitted by the radar gun?
b) How much did the frequency of the radio waves change when they bounced off of your car? Give a number and say whether the frequency got bigger or smaller.
c) For the policeman to be able to measure your speed with an accuracy of 1 mph, how small would the fractional uncertainty in his measurement have to be? (That is the ratio of the uncertainty in his measurement of the frequency of the radio wave to its frequency.) You might speculate on how a radar gun could make such a precise measurement.

3. Radio station KXYZ broadcasts at a frequency of 100 MHz. It broadcasts a power of 100 kWatt (that is 100,000 Joules per second). How many radio wavelength photons does it emit each second?

1 October 2003
Astronomy Program · The University of Texas at Austin · Austin, Texas 78712
prospective student inquiries: studentinfo@astro.as.utexas.edu