Sample Exam

PHYSICS 213 – PRACTICE EXAM 3*
*The actual exam will contain EIGHT multiple choice quiz-type questions covering
concepts from lecture (16 points), ONE essay-type question covering an important
fundamental principle from lecture (4 points), and FOUR problems similar to the
problems that follow (80 points).
NAME (printed)
SIGNATURE
Student Number
SECTION
INSTRUCTIONS
Wait for oral instructions before starting the test.
Remember to show (in English) your problem solving steps for
FULL CREDIT.
A calculator and a one-sided 8½X11 student reference sheet are
permitted. Your reference sheet may contain equations, graphs,
and notes; however, quiz questions and worked out problems
CANNOT be included. Cell phones/communication devices must
be put away.
For the graders:
Q1-9
P1
P2
P3
P4
TOTAL

Electromagnetic Waves [20 Points]
A large parabolic solar detector with radius 25.0 m is mounted to a solar
probe with total mass 2500 kg which is placed in space near the Earth’s
orbit. The solar detector absorbs solar radiation with intensity 1340 W/m 2 .
a) Find the amplitude of the electric field for the solar radiation? [5 points]
Answer: E = 1005 V/m
b) Find the amplitude of the magnetic field for the solar radiation? [4 points]
Answer: B = 3.35 µT
c) Determine the solar power absorbed by the solar detector. [3 points]
Answer: P = 2.63 MW
d) Ignoring all gravitational effects, determine the acceleration of the solar
probe due to the soar radiation pressure. [4 points]
Answer: a = 3.51 x 10 -6 m/s 2
e) Find the probe’s speed as it reaches Mars 7.80 x 10 10 m away. Ignore all
gravitational effects and assume the probe starts from rest and the solar
intensity remains constant. [4 points]
Answer: v = 740 m/s

Snell’s Law [20 Points]
A beam of light passes through different layers of materials with different
indices of refraction as shown in the figure.
a) If the beam emerges at θ 2 = 50°, find the incident angle θ 1 . [8 Points]
Answer: θ 1 = 28.6°
b) What must be the incident angle θ 1 in order to have total internal
reflection occur at the bottom surface between the medium with n = 1.20
and the medium with n = 1.00? [6 Points]
Answer: θ 1 = 38.7°
c) If total internal reflection occurs at the bottom and top surfaces (when the
incident angle is what you calculated in part b), how many reflections will
occur between the top and bottom surfaces if all layers are 5.00 m in
length and 25.0 cm in width? [6 Points]
Answer: N = 6.00 reflections

Dispersion and Total Internal Reflection [20 Points]
As shown below, white light is incident normally on a face of a 30 o -60 o -90 o
flint prism (n 1 = 1.655 for violent light and n 1 = 1.595 for red light), that is
immersed in water (n 2 = 1.333). The ray undergoes total internal reflection
at point P.
n 2
60
n 2
P
n 1
n 2
θ
a) Determine the exit angle θ for red and violet light. What is the dispersion
of the prism? [14 Points]
Answer: θ red = 36.7°, θ violet = 38.4°, and Δθ = 1.7°
b) A substance is dissolved in the water to increase the index of refraction.
At what value of n 2 of the mixture will total internal reflection cease at
point P for red and violet light? [6 Points]
Answer: n 2 = 1.381 (red) and n 2 = 1.433 (violet)

Mirrors [20 Points]
I) High school kids are always worried about pimples. When I was an
adolescent, I had one of those magnifying shaving mirrors with which I
perused my physiognomy diligently. If you place your face 15 cm from
the mirror, what focal length is required to provide a magnification of
1.33? Draw the convenient type of mirror (concave or convex) and draw
the rays. [10 Points]
Answer: 60 cm and concave mirror
II) An object is placed at a distance of p = 20 cm in front of a convex mirror
of focal length f = -10 cm as shown.
a) Where is the image located with respect to the mirror? Is the image
virtual or real? Inverted or upright? [6 Points]
Answer: 6.67 cm behind the mirror, virtual, upright
b) What is the magnification of the mirror? [4 Points]
Answer: M = 0.333

Combination of Lenses [20 Points]
The object is placed 60 cm in front of a diverging lens with a focal length of
-15 cm. A converging lens of focal length 20 cm is placed 10 cm behind the
first lens.
a) Make a diagram indicating the position of the lenses, the object and final
image, and the corresponding distances measured from the origin.
Assume the optical system is along the x-axis and take x = 0, as the
position of the diverging lens. [10 Points]
Answer: Final image is real, inverted at 230 cm. Diagram is shown.
b) Find the magnification of the two lens system. [4 Points]
Answer: M = -2
c) Repeat parts a) and b) for the case when the object is placed 10 cm in
front of the diverging lens. [6 Points]
Answer: Final image is virtual, upright at -70 cm with M = 3

Interference [20 Points]
An airplane is traveling 100 m above two radio
transmitters with the same height and a
distance d = 5.00 m apart. The radio signal
emitted from both transmitters has a
wavelength of λ = 75.0 cm. The signal
received by the airplane can be used to
determine the location of the airplane with
respect to the midpoint between the two
transmitters.
a) Determine how far the airplane is from the
midpoint between the two transmitters if
the radio signal received is at the third
maximum? [8 Points]
Answer: 112 m
b) Determine how much further the airplane must travel horizontally to
reach the next maximum. [6 Points]
Answer: 24.6 m
c) Suppose the space in which the waves are traveling is replaced with
seawater of refractive index n = 1.35 and the airplane is replaced by a
submarine. What would be the answer to parts a) and b)? [6 Points]
Answer: 106 m, 14.3 m

Diffraction [20 Points]
The emission of light from an excited gas is focused and passed through a
diffraction grating with 3000 lines/cm, as shown. First order and second
order spectral lines are observed.
a) Four first-order spectral lines are observed at 7.07°, 7.48°, 8.38°, and
11.3°. Find the wavelengths of these four spectral lines. [8 Points]
Answer: λ 1 = 410 nm, λ 2 = 434 nm, λ 3 = 486 nm, and λ 4 = 656 nm
b) At what angles are the second-order spectral lines observed? [7 Points]
Answer: θ 1 = 14.2°, θ 2 = 15.1°, θ 3 = 17.0°, and θ 4 = 23.2°
c) Suppose the diffraction grating is replaced with another having twice the
number of gratings/cm. Find the angular separation observed between
the second-order spectral lines. [5 Points]
Answer: Δθ = 22.5°

Polarization [20 Points]
Three polarizing plates whose planes are parallel are centered on a common
axis. The directions of the transmission axes relative to the common vertical
direction are shown in the figure. A linearly polarized beam of light with
plane of polarization parallel to the vertical reference direction is incident
from the left onto the first disk with intensity I i = 100 W/m 2 .
a) Determine the transmitted intensity I f when θ 1 = 10.0°, θ 2 = 30.0°, and
θ 3 = 60.0°. [7 Points]
Answer: I f = 64.2 W/m 2
b) What is the ratio I f /I i of the final transmitted intensity to the incident
intensity if θ 1 = 30.0°, θ 2 = 60.0°, and θ 3 = 90.0°? [7 Points]
Answer: I f /I i = 27/64
c) If θ 1 = 0° and θ 2 = 45.0°, what should θ 3 be in order to make I f /I i = 3/8?
[6 Points]
Answer: θ 3 = 75.0°