Problem Set 4
Due: See Website for due dates
Chapter 33: Electromagnetic Waves
Exercises & Problems: 2, 16, 33, 40, 46, 55, 60, 63, 76, 90
Question A
Explain in detail how electromagnetic waves can be created by an accelerating electric
charge using Maxwell’s equations.
Question B
When light waves enter a medium of higher refractive index than the previous, why is it
that (i) frequency stays the same? (ii) Wavelength decrease? (iii) Speed decreases?
Question C
Using the dielectric model of the atom, explain why (i) glass is transparent for optical
frequencies but is opaque for UV and IR frequencies? (ii) How is light transmitted
through clear glass?
Question D
What I the difference between a mirror and a white sheet?
Question E
It has been proposed that automobile windshields and headlights should have polarizing
filters to reduce the glare of oncoming lights during night driving. Would this work? How
should the polarizing axes be arranged? What advantages would this scheme have?
What disadvantages?
Problem 33.2
Project Seafarer was an ambitious program to construct an enormous antenna, buried
underground on a site about 10 000 km2 in area. Its purpose was to transmit signals to
submarines while they were deeply submerged. If the effective wavelength were 104
Earth radii, what would be the (a) frequency and (b) period of the radiations emitted?
Ordinarily, electromagnetic radiations do not penetrate very far into conductors such as
seawater, and so normal signals cannot reach the submarines.
Problem 33.16
Frank D. Drake, an investigator in the SETI (Search for Extra-Terrestrial
Intelligence) program, once said that the large radio telescope in Arecibo,
Puerto Rico, “can detect a signal which lays down on the entire surface of
the earth a power of only one picowatt.” (a) What is the power that would
be received by the Arecibo antenna for such a signal? The antenna
diameter is 300 m. (b) What would be the power of an isotropic source at
the center of our galaxy that could provide such a signal? The galactic center is 2.2 ×104
ly away, where ly ≡ light-year is the distance light travels in one year.
Problem 33.33
In the figure, initially unpolarized light is sent into a system of three
polarizing sheets whose polarizing directions make angles of θ1 = 40°,
θ2 = 20°, and θ3 = 40° with the direction of the y axis. What
percentage of the light’s initial intensity is transmitted by the system?
(Hint: Be careful with the angles.)
Problem 33.40
In the figure, unpolarized light is sent into a system of three polarizing sheets. The
angles 1, 2, and 3 of the polarizing directions are measured counterclockwise from the
positive direction of the y axis (they are not drawn to scale).
Angles 1 and 3 are fixed, but angle 2 can be varied. The
figure gives the intensity of the light emerging from sheet 3 as
a function of 2. (The scale of the intensity axis is not
indicated.) What percentage of the light’s initial intensity is
transmitted by the three-sheet system when 2 = 90°?
Problem 33.46
In figure (a), a light ray in an underlying material is
incident at angle 1 on a boundary with water, and
some of the light refracts into the water. There are
two choices of underlying material. For each, the
angle of refraction 2 versus the incident angle 1 is
given in figure (b). The horizontal axis scale is set by
1S = 90°. Without calculation, determine whether the
index of refraction of (a) material 1 and (b) material 2
is greater or less than the index of water (n = 1.33).What is the index of refraction of (c)
material 1 and (d) material 2?
Problem 33.55
In the figure, a 2.00-m-long vertical pole extends from the bottom of a
swimming pool to a point 50.0 cm above the water. Sunlight is incident at
angle  =55.0°. What is the length of the shadow of the pole on the level
bottom of the pool?
Problem 33.60
In Fig. 33-58, light from ray A refracts from material 1 (n1 = 1.60) into a thin layer of
material 2 (n2 =1.80), crosses that layer, and is then incident at the
critical angle on the interface between materials 2 and 3 (n3 = 1.30). (a)
What is the value of incident angle θA? (b) If θA is decreased, does part of
the light refract into material 3?
Light from ray B refracts from material 1 into the thin layer, crosses that
layer, and is then incident at the critical angle on the interface between
materials 2 and 3. (c) What is the value of incident angle θB? (d) If θB is
decreased, does part of the light refract into material 3?
Problem 33.63
In the figure, light enters a 90° triangular prism at point P with incident
angle θ, and then some of it refracts at point Q with an angle of
refraction of 90°. (a) What is the index of refraction of the prism in terms
of θ? (b) What, numerically, is the maximum value that the index of
refraction can have? Does light emerge at Q if the incident angle at P is
(c) increased slightly and (d) decreased slightly?
Problem 33.76
In the figure, unpolarized light with an intensity of 25 W/m2 is sent
into a system of four polarizing sheets with polarizing directions at
angles θ1 = 40°, θ2 = 20°, θ3 = 20°, and θ4 = 30°.What is the
intensity of the light that emerges from the system?
Problem 33.90
In the figure, two light rays pass from air through five layers of transparent plastic and
then back into air. The layers have parallel interfaces and unknown thicknesses; their
indexes of refraction are n1 = 1.7, n2 = 1.6, n3 = 1.5, n4 = 1.4, and n5 = 1.6. Ray b is
incident at angle θb = 20°. Relative to a normal at the last interface, at what angle do (a)
ray a and (b) ray b emerge? (Hint: Solving the problem algebraically can save time.) If
the air at the left and right sides in the figure were, instead, glass with index of refraction
1.5, at what angle would (c) ray a and (d) ray b emerge?