Leo Radzihovsky, Spring, 2013
PHYS 1230: Light and Color
Homework Solutions Set 3
Issued January 29, 2013
Due February 5, 2013
(turn into Phys1230 collection box in Help Room, G2B90)
Reading Assignment: Ch.2 of “Seeing the Light” (SL), Falk, Brill, Stork; class lecture notes
1. If you observe thunder and lightning, you can tell (with pretty good accuracy) how far
away the storm is. Do you need to know the speed of sound, of light, or of both?
You need to know the speed of sound but you can approximate that the light gets
to you instantly (in some sense, that it has infinite velocity).
How would you approximately figure out the distance?
You could measure the time between when you see the light and when you hear the
sound. Then you could calculate how far the sound could travel in that amount of
time by multiplying v × t. This distance is approximately how far away the lightning
was.
What measurement would you make to do this?
You would measure the time between seeing the lighting and hearing the thunder.
2. Laser beams are made of light. In science fiction movies, laser beams are often shown
as bright lines shooting out of a laser gun on a spaceship. Briefly state why this is
scientifically incorrect.
We only see light rays that actually enter our eyes. Laser beams are made of rays
that all point in one direction (they are collinear). Therefore, you could only see the
beam if it was pointed straight into your eye- you couldn’t see it from the side unless
some rays interact with air particles and get deflected, or scattered into your eye.
3. A Global Positioning System (GPS) receiver (e.g., in your i-phone or car) is a device
that lets you figure out where you are by receiving timed radio signals from satellites
in orbit above the earth. It works by measuring the travel time for the electromagnetic
signals, which is related to the distance between you and the satellite. By finding
the ranges to several different satellites in this way, it can pin down (triangulate)
your location in three dimensions to within a few meters. How accurate does the
measurement of the time travel to/from satellite have to be to determine your position
to this accuracy? (A simple estimate is sufficient)
Hint: distance = speed x time (d = v t)
Here, we want to find out how long it takes for light to travel a few meters. This
will tell us how inaccuracies in the time measurement will affect the position readout.
d = 3m (we’ll find the time for light to travel 3 meters.)
d/v = t
3m/3 ∗ 108 m/s = 1 ∗ 10−8 s or 10 nanoseconds
Tens of nanoseconds is the temporal accuracy needed to get within a few meters of
spatial accuracy.
4. Estimate the frequency of an electromagnetic wave whose wavelength is similar in size
to an atom (about a 1nm). Referring back to figures in the notes of lectures 1 and
2 and/or table 1.1 on pg 17 of your SL text 24.5.3 on p. 675, in what part of the
electromagnetic spectrum would such a wave lie (infrared, gamma-rays, ...)?
f = c/λ = 3 ∗ 1017 Hz This is in the upper end of the ultraviolet part of the spectrum, verging on the x-ray part.
5. A camera using a lens has a much larger hole than the pinhole camera (that we discussed in class) has. (a) Without knowing anything about lenses, why would you want
to have a large hole rather than the tiny pinhole?
A large hole emits more light than a tiny hole, so the picture takes less time to expose
(b) We’ve seen what happens to the image in the pinhole camera when the pinhole is
made larger. What do you think the purpose of the lens is in a regular camera?
The lens bends the light so that it all of the rays coming from one point on an object
hit the film in the same place. This is called focusing
6. The figure on pg.69 Ch. 2 of the SL text (above problem P7) shows a pinhole camera photographing two arrows. (a) How do the size of the images of the two arrows
compare? (b) Which arrow’s image will be pointing up?
Hint: It may be useful to redraw the figure, use a straight edge to draw the light rays
and use a ruler to make your measurements to answer part (a).
The arrow labeled a in the book will be upside down and the arrow labeled b will
be upright. The size is somewhat ambiguous. The larger arrow would be taller if they
were at the same distance from the pinhole, but more distant objects look shorter so
the overall heights are similar.
7. The man in the figure of problem P13, pg. 69 of your SL text is looking at himself in a
triple mirror found in a clothing store. Redraw the figure and show two different rays
of light that go from his right ear to his left eye. One ray should hit only one mirror,
the other ray should hit the other two mirrors. At each reflection, draw the normal
(perpendicular) to the mirror, and label θi and θr that the ray makes relative to the
normal.
Hint: The correct rays have to have the incidence and reflected angles with the normal
to the mirror equal.
8. Briefly explain how an oceanographer might use sonar to measure the depth of the
ocean.
Sound waves propagate through water, but largely reflect when they hit the denser
ground beneath it. One could send sound waves straight down, and measure the time
that it takes for them to return. Then calculate the distance traveled by sound in that
time. This would give the round trip travel distance to the bottom of the ocean and
back.
9. Blue light bends more than red light when entering glass from air because: (a) red
light travels faster than blue light in glass, (b) blue light travels faster than red light
in glass, (c) red light travels faster than blue light in air, (d) blue light travels faster
than red light in air.
(a) Refraction occurs because light slows down when it enters media with higher indexes of refraction. Dispersion (spreading out of the different colors of light) happens
because light with a short wavelength interacts more with the material than light with
a long wavelength and slows down more because of it.
10. Why does the sun appear above the horizon when it is actually below the geometrical
horizon during a sunset?
Hint: The answer lies in the refraction through the atmosphere that gets thinner (i.e.,
closer to vacuum) as you go up above the earth. It helps to draw a picture of a section
of a spherical earth, draw a horizontal line from your point toward the sun setting
below this horizontal (horizon) and think about how the light rays from the setting sun
can possibly get to your eyes, even though the sun is physically below the horizon.
As can be seen from the picture below, rays coming from below the sun would have
to bend toward the Earth to be seen from point A. This happens because as a ray
coming from outer space (essentially a vacuum) hits the gradually denser and denser
atmosphere, it gradually bends toward the normal. This causes it to arc around the
earth and into your eye.