### Spring 2006 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 117. The exam period was 90 minutes; the mean was 89.8; the median was 91. Click here to see page1 page2 of the formula sheet that came with the exam.

• A physics 102 light bulb acts just like a resistor: its resistance is constant, independent of the current flowing through the light bulb. The bulb's brightness increases with increasing current.
• 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 and the next question both pertain to this figure:

What is the resonance frequency for this circuit?

(a)   5 × 107 Hz
(b)   2 × 107 Hz
(c)   104 Hz
(d)   1125 Hz
(e)   607 Hz

### QUESTION 2**

What would be the average power dissipated in the circuit if the generator were tuned to the resonance frequency?

(a)   40 W
(b)   60 W
(c)   80 W

### QUESTION 3**

The SiD silicon detector experiment for the International Linear Collider consists of a solenoid which is 5 m long and 5 m in diameter, as shown, and produces a homogeneous magnetic field of 5 tesla.

What is the total energy stored in this solenoid (neglecting fringe effects)?

(a)   1.3 J
(b)   35 J
(c)   1280 J
(d)   5.6 × 104 J
(e)   9.76 × 108 J

### QUESTION 4*

This and the next two questions concern the following situation:

Vertically polarized light with intensity I0 is incident on a series of three polarizers, as in the figure below. The middle polarizer may be rotated to any angle, θ.

For which value of θ will the most light be transmitted?

(a)   45°
(b)   22.5°
(c)   0 °

### QUESTION 5**

What is the transmitted intensity if θ = 10° ?

(a)   0.11 I0
(b)   0.22 I0
(c)   0.33 I0

### QUESTION 6*

What is the transmitted intensity if the middle polarizer is removed?

(a)   0.7071 I0
(b)   0

### QUESTION 7*

This and the next question concern the following situation:

An electromagnetic wave with frequency f = 6.15 × 1014 Hz is traveling in vacuum at a speed c = 3 × 108 m/s. The wave strikes a 9 cm2 (9 × 10-4 m2) surface oriented perpendicular to the wave, depositing 1.35 mW of average power.

What is the wavelength of this wave?

(a)   360 nm
(b)   488 nm
(c)   530 nm
(d)   624 nm
(e)   1250 nm

### QUESTION 8***

What is the average total energy density in the wave?

(a)   8 × 10-5 J/m3
(b)   1 × 10-6 J/m3
(c)   6 × 10-7 J/m3
(d)   2 × 10-8 J/m3
(e)   5 × 10-9 J/m3

### QUESTION 9*

A ray of blue light and a ray of red light strike the same point on the surface of a plastic block at slightly different angles θblue = 46° and θred = 45° as shown in the figure. The plastic is dispersive (its index of refraction varies with wavelength) so the two light rays are refracted through different angles as they enter the plastic. It is found that they travel along exactly the same path inside the plastic, making an angle θboth = 35° with respect to the normal to the interface.

If the indices of refraction for blue and red light are nblue and nred respectively, what is their difference, nblue - nred ?

(a)   1.334
(b)   -0.333
(c)   0.0213
(d)   0.0169
(e)   0.0286

### QUESTION 10*

In the following diagrams, mirrors (hidden from your view by the gray rectangles) reflect light rays. Some (or all) of the mirrors might be concave with radii of curvature +2 m and focal length +1 m; some (or all) might be convex with radii of curvature -2 m and focal length -1 m. Not all of the diagrams are correct.

Assuming that each mirror is properly centered at x = 0, which of the diagrams are correct?

(a)   1 and 2
(b)   1 and 3
(c)   2 and 3
(d)   2 and 4
(e)   3 and 4

### QUESTION 11*

This and the next question concern the following situation:

A candle is placed 15 cm away from a convex mirror with radius of curvature -20 cm and focal length f = -10 cm as shown in the figure.

The image formed by the mirror is

(a)   upright and reduced and virtual.
(b)   inverted and enlarged and real.
(c)   inverted and reduced and virtual.
(d)   upright and enlarged and real.
(e)   upright and reduced and real.

### QUESTION 12*

The location of the image is

(a)   30 cm to the left of the mirror.
(b)   10 cm to the right of the mirror.
(c)   6 cm to the right of the mirror

### QUESTION 13**

This and the next question concern the following situation:

A sandwich is made from two layers of flat, transparent cladding with index of refraction ncladding placed above and below a flat transparent core with index of refraction ncore. A laser beam travels through the core at an angle θbeam with respect to the normal to the core-cladding boundary as shown in the figure. The beam undergoes total internal reflection at the interfaces between the cladding and the core.

If θbeam becomes too small the beam will no longer undergo total internal reflection at the interface between the core and the cladding.

(T)   True
(F)   False

### QUESTION 14*

Imagine that a technician varies the angle θbeam between 0° and 90°. If ncladding = 1.3 and ncore = 1.5, what angle θbeam corresponds to the transition from total internal reflection at the core-cladding interface to escape of the beam from the core?

(a)   78.0°
(b)   60.1°
(c)   78.5°

### QUESTION 15*

This and the next question concern the following situation:

A two-lens device is made from a convex lens with focal length f1 = 10 cm and a concave lens with focal length f2 = -20 cm as shown in the following figure. A candle is placed 15 cm to the left of the convex lens. The image of the candle formed by the first lens serves as an object for the second lens which, in turn forms an image from this object. The lenses are 60 cm apart.

What is the position of the image formed by the concave lens?

(a)   45 cm to the right of the concave lens
(b)   40 cm to the left of the concave lens
(c)   20 cm to the left of the concave lens
(d)   15 cm to the right of the concave lens
(e)   12 cm to the left of the concave lens

### QUESTION 16**

The concave lens makes an image of the lit candle. In this image,

(a)   the candle's base is closer to the ceiling than is its flame -- the image is real.
(b)   the candle's base is closer to the ceiling than is its flame -- the image is virtual.
(c)   the candle's flame is closer to the ceiling than is its base -- the image is real.
(d)   the candle's flame is closer to the ceiling than is its base -- the image is virtual.
(e)   neither the flame nor the base is closer to the ceiling since the image is a point.

### QUESTION 17*

This and the next question concern the following situation:

The eyes of a patient in need of corrective lenses are slightly prolate so that the distance from the cornea to the retina is greater than the focal length of the combination of the cornea and relaxed lens, as shown in the figure. As a result, parallel rays from a very distant object focus 25 mm from the front of the eye, even though the retina is 27 mm from the front of the eye.

What kind of corrective lens is needed to allow the patient to focus on distant objects?

(a)   converging
(b)   diverging

### QUESTION 18*

Without wearing corrective lenses, what is the farthest distance for an object that can be seen clearly by the patient when his/her lens is relaxed?

(a)   2 mm
(b)   52 mm
(c)   104 mm
(d)   337.5 mm
(e)   675 mm

### QUESTION 19**

This and the next two questions concern the following situation:

Two slits spaced by 0.3 mm are placed 50 cm away from a screen. The slits are illuminated with light whose wavelength is 600 nm.

What is the distance between second and third dark lines of the interference pattern?

(a)   2 mm
(b)   0.3 mm
(c)   1 mm
(d)   0.2 mm
(e)   0.5 mm

### QUESTION 20*

If the number of slits is increased from two to ten but, but the spacing between adjacent slits kept at 0.3 mm, which one of the following would be true?

(a)   The distance between two consecutive main maxima would increase.
(b)   The distance between two consecutive main maxima would decrease.
(c)   This will not affect the distance between twoconsecutive main maxima.

### QUESTION 21**

If I2 is intensity of the interference maximum provided by two slits, the intensity of a line in the case of 10 slits would be:

(a)   I2
(b)   5 I2
(c)   25 I2

### QUESTION 22**

This and the next question concern the following situation:

A laser printer creates an image by printing small but discrete dots on a page. If the printer used only red ink ( λ = 600 nm), how small would the spacing between dots have to be, in units of dpi (dots per inch; 1 in. = 2.54 cm), for the image to look smooth? Assume your eyes are 25 cm from the page and that your pupil is round and is 2.0 mm in diameter.

(a)   556 dpi
(b)   1200 dpi
(c)   278 dpi
(d)   139 dpi
(e)   1110 dpi

### QUESTION 23**

How would your answer change if the printer used blue ink ( λ = 400 nm)?

(a)   The spacing between dots would have to be smaller.
(b)   The spacing between dots could be larger.
(c)   The needed spacing would not change.

### QUESTION 24***

This and the next question concern the following situation:

An interference maximum for the scattering of a beam of X-rays of wavelength 0.156 nm occurs when the angle θ between the beam and the surface of the crystal is 12.8°. The maximum is due to scattering from the atoms in planes parallel to the crystal surface. Assuming that it is a first order maximum, determine the interplanar spacing, d.

(a)   0.704 nm
(b)   0.352 nm
(c)   0.532 nm

### QUESTION 25*

The crystal is heated and it expands thermally, resulting in a larger value of d. Which one of the following is correct?

(a)   This results in an increase in the angle θ.
(b)   This results in a decrease in the angle θ.
(c)   This will not affect θ.

### QUESTION 26*

This and the next question concern the following situation:

Light of wavelength 600nm is incident on a long, narrow slit of width w, as shown in diagram (a). This slit produces a diffraction pattern on a screen 1 m away, as illustrated in diagram (b).

What is the width of the slit?

(a)   0.6 μm
(b)   1.2 μm
(c)   1.8 μm
(d)   2.4 μm
(e)   3.0 μm

### QUESTION 27*

If the width of the slit were doubled, what would happen to the location of the first minimum on the screen?

(a)   It would shift to a larger angle.
(b)   It would shift to a smaller angle.
(c)   The position of the minimum would not change.

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.