Problem 1 (5 Points)
In the first application of
interferometric methods in radio
astronomy, Australian astronomers
observed the interference between a
radio wave arriving at their antenna
directly from the Sun and on a path involving reflection from the surface of the sea.
Assume that radio waves have a frequency of 6.0 ¡Á 107 Hz, and that the radio receiver is
25 m above the surface of the sea. What is the smallest angle ¦È above the horizon that
will give destructive interference of the waves at the receiver?
Problem 2 (8 Points)
The figure to the right shows a Mach-
Zehnder interferometer. Invented over 100
years ago, it is still used for many optical
measurements.
Light form a point source in the lower-left
strikes a half-silvered mirror, which
reflects half the light incident on it and
transmits half the incident light. The two
split beams, U and D, strike good mirrors which directs the rays to another half silvered
mirror. This second half-silvered mirror splits the combined beams, directing half to
detector 1 and the other half to detector 2. The detectors are indicated as half-circles.
The device is constructed so that the light rays travel the same distance from where they
are split by the 1st ¡°beam splitter¡± until they are combined at the 2nd one.
What fraction of the light from the source enters detector 1?
Problem 3 (4 Points)
A converging lens has a focal length f, and a diverging
lens has a focal length ¨Cf, which has the same magnitude
as the converging lens. They are separated by a distance
D which is greater than f, as shown. Parallel light enters
from the left. Will the light be brought to a focus, and if
so where?
Problem 4 (3 Points)
Imagine that the parallel light rays in Problem 3 enter from the right. Explain why the
light will be brought to focus without using any equations.
2 answers
4 answers