Spring 2010 Physics 102 Hour Exam 3(27 questions)

The grading button and a description of the scoring criteria are at the bottom of this page.Basic questions are marked by a single star *. More difficult questions are marked by two stars **. The most challenging questions are marked by three stars ***.

True-false questions are worth 2 points each, three-choice multiple choice questions are worth 3 points each, five-choice multiple choice questions are worth 6 points each. The maximum possible score is 116. The exam period was 90 minutes; the mean score was 94.2; the median was 98. Click here to see page1 page2 page3 of the formula sheet that came with the exam.

• A reminder about prefixes: p (pico) = 10-12; n (nano) = 10-9; μ (micro) = 10-6; m (milli) = 10-3; k (kilo) = 10+3; M or Meg (mega) = 10+6; G or Gig (giga) = 10+9.

QUESTION 1*

This question and the next three pertain to the the following situation.

An optical fiber consists of a small cylinder of glass called the core, shown in gray, surrounded by a layer of glass called the cladding. Light rays entering the fiber propagate as shown. The index of refraction of the core is n = 1.444 . The intensity of the light in the fiber is 1.3 × 108 W/m2.

If the maximum angle off-axis θ with which a ray can propagate in the fiber is 4°, what is the index of refraction of the cladding?

(a)   1.44
(b)   1.53
(c)   1.71

QUESTION 2*

If the ray is traveling at the maximum off-axis angle after entering the fiber as shown, at what angle α did it enter the fiber?

(a)   2.3°
(b)   4.0°
(c)   5.8°

QUESTION 3*

For one type of optical fiber, the diameter of the core is 10 μm. What is the power of the light in this fiber?

(a)   10 mW
(b)   40 mW
(c)   62 mW

QUESTION 4*

What is the speed of light inside the fiber?

(a)   1.2 × 108 m/s
(b)   2.1 × 108 m/s
(c)   4.3 × 108 m/s

QUESTION 5*

What is the minimum vertical length of a flat mirror if an alien from outer space wants to see her whole body in the mirror? Note that her eyes are located at the top of her head.

(a)   half the height
(b)   ¾ of the height
(c)   same height
(d)   slightly longer than the height
(e)   twice the height

QUESTION 6*

An unpolarized light source impinges on two linear polarizers. The final intensity is 1/10 of the original intensity. What must be the angle between the transmission axes of the two polarizers?

(a)   13.1°
(b)   51.6°
(c)   63.4°
(d)   78.5°
(e)   84.2°

QUESTION 7**

Your physics 102 professor is near-sighted and requires corrective lenses. His far point is 20 cm. What refractive power lens does he need?

(a)   -20 diopters
(b)   -5 diopters
(c)   0.05 diopters
(d)   5 diopters
(e)   20 diopters

QUESTION 8*

This question and the one pertain to the the following situation.

Two lenses are indicated below. The convex lens has a focal length of 11 cm and the concave lens has a focal length of -17 cm. The object is located 14.1 cm to the left of the convex lens.

Where is the final image located with respect to the concave lens? Standard sign conventions apply.

(a)   -10.1 cm
(b)   24.3 cm
(c)   32.0 cm
(d)   44.9 cm
(e)   60.4 cm

QUESTION 9**

The final image is

(a)   upright.
(b)   inverted.

QUESTION 10*

This question and the one pertain to the the following situation.

A sodium light bulb is analyzed with a diffraction grating. The slits of the grating have a separation of 1000 nm. The sodium light has two closely spaced emission lines, whose wavelengths are 589.0 nm and 589.6 nm.

What is the angle Δθ between the first-order maxima corresponding to 589.0 nm and the first-order maxima of 589.6 nm?

(a)   0°
(b)   0.043°
(c)   0.31°
(d)   4.3°
(e)   36.2°

QUESTION 11*

What is the angle corresponding to the second-order maximum for the first sodium line at 589.0 nm?

(a)   45.3°
(b)   65.9°
(c)   There is no second-order maximum.

QUESTION 12*

This question and the one pertain to the the following situation.

A vertically polarized beam of light goes through a system of 5 polarizers. The first polarizer is oriented at 18° from the vertical, and the transmission axis of each successive polarizer is oriented 18° from the previous one.

The emerging beam from the five polarizers has an intensity of 30 W/m2. What is the intensity of the incident light?

(a)   24.78 W/m2
(b)   38.56 W/m2
(c)   49.55 W/m2

QUESTION 13**

A square solar cell of side L=10 cm receives light emerging from the polarizers. How much energy will the solar cell collect if illuminated for 1 minute?

(a)   0.3 J
(b)   1.8 J
(c)   18 J
(d)   29.7 J
(e)   180000 J

QUESTION 14**

This and the next two questions pertain to the the following situation.

A series RLC circuit is driven by a generator with voltage V(t) = 10 sin(100t) volts. At some instant t0, the voltage of the generator was observed to be at its maximum (positive) value. Which one of the following could correctly represent the phasor diagram of this circuit at this instant of time?

(a)
(b)
(c)

QUESTION 15*

If L = 30 mH, R = 2 Ω, and C = 15 mF and the driving generator has voltage V(t) = 10 sin(100t) volts, what is the angle that the voltage across the generator makes relative to the voltage across the resistor?

(a)   9.1°
(b)   20.2°
(c)   49.4°
(d)   51.3°
(e)   88.0°

QUESTION 16**

What is the average power dissipated by the circuit when driven at the resonance frequency given the circuit has component values L = 30 mH, R = 2 Ω, C = 15 mF and the generator has voltage V(t) = 10 sin(ωt) volts?

(a)   Paverage = 2.72 watts
(b)   Paverage = 3.14 watts
(c)   Paverage = 5.11 watts
(d)   Paverage = 10.5 watts
(e)   Paverage = 25.0 watts

QUESTION 17*

An unpolarized light source impinges on a system of two linear polarizers from left to right. The orientation of their transmission axes is unknown. It is observed that the intensity of the light after it has passed the system of polarizers is equal to I1 = 1/4 I0, where I0 is the original intensity on the polarizers.

What is I1 after sending unpolarized light with intensity I0 through the same system of polarizers but in the opposite direction (from right to left)?

(a)   ¼ I0
(b)   ½ I0
(c)   0

QUESTION 18*

A laser emits a beam of light with an intensity of 0.3 W/m2. What is the value of Brms for the light?

(a)   1.73 nT
(b)   2.54 nT
(c)   6.47 nT
(d)   15.5 nT
(e)   35.4 nT

QUESTION 19*

This question and the next three pertain to the the following situation.

A radio wave (1 MHz) is transmitted around town from a nearby tower. The electromagnetic wave can be represented by the following picture.

What is the wavelength of the signal?

(a)   100 m
(b)   150 m
(c)   200 m
(d)   300 m
(e)   not enough information

QUESTION 20**

What is the polarization direction of this signal?

(a)   in the +x direction
(b)   in the +z direction
(c)   in the -y direction

QUESTION 21*

What is the direction of propagation of the wave?

(a)   x direction
(b)   y direction
(c)   z direction

QUESTION 22*

The amplitude of this electric field Emax = 0.314 V/m. The amplitude of the magnetic field is

(a)   1.0 × 10-9 T
(b)   2.3 × 10-7 T
(c)   5.0 × 10-6 T

QUESTION 23*

This and the next two questions pertain to the the following situation.

Consider an object 2 cm in height placed 15 cm in front of a concave mirror of focal length f = 5 cm, as shown in this figure.

Which one of the rays in the picture is incorrect?

(a)   ray 1
(b)   ray 2
(c)   ray 3

QUESTION 24*

What is the magnification?

(a)   -2
(b)   -0.5
(c)   0
(d)   0.5
(e)   2

QUESTION 25*

A piece of black tape is placed over the top half of the mirror surface (above the principal axis P.A.) preventing any reflection there. Which one of the following statements is true?

(a)   Only the top half of the object is imaged.
(b)   Only the bottom half of the object is imaged.
(c)   The whole object is imaged, but the image is dimmer.

QUESTION 26*

Unpolarized light traveling through water is incident on a flat crystal surface. The light reflects off completely polarized at a unique angle α with the surface of the crystal as shown below. The refractive index of water is nW = 1.33 and that of the crystal is nC = 1.5 .

What is the angle α ?

(a)   17.8°
(b)   41.6°
(c)   72.2°

QUESTION 27*

Two thin films of transparent material with indices of refraction n2 and n3 are stacked as shown in the figure. The bottom face of the lower sheet is coated with a light-absorbing material so that no light can reflect off this face.

An argon-ion laser produces visible light of wavelength λ = 514 nm in air which strikes the top surface of the upper film. The incident light ray is actually vertical. The thickness of the material with index n2 is d.

Which minimum value of d can produce a bright reflected beam?

(a)   d = 10 nm
(b)   d = 34 nm
(c)   d = 69 nm
(d)   d = 137 nm
(e)   d = 215 nm

Scoring of True-False (T,F) Questions:
• If you mark the correct answer, you get 2 points.
• If you mark the wrong answer or if you mark neither answer, you get 0 points.
Scoring of Multiple Choice I (a,b,c) Questions:
• If you mark the correct answer, you get 3 points.
• If you mark a wrong answer or if you mark none of the answers, you get 0 points.
Scoring of Multiple Choice II (a,b,c,d,e) Questions:
• If you mark one answer and it is the correct answer, you get 6 points.
• If you mark two answers and one of them is the correct answer, you get 3 points.
• If you mark three answers and one of them is the correct answer, you get 2 points.
• If you do not mark the correct answer, or if you mark more than three answers, or if you mark none of the answers, you get 0 points.