Question
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.
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.
Answers
bobpursley
I am not inclined to work these out for you.. Indicate your thinking in words, and I will critique. Reminder: on the first one, is there a phase shift upon reflection?
Tdotjace
Jimmy goes to uoft!