### Fall 2005 Physics 102 Hour Exam 3(28 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 122. The exam period was 90 minutes; the mean was 102.6; the median was 104. Click here to see page1 page2 of the formula sheet that came with the exam.

### QUESTION 1*

When light travels from a medium with index of refraction n1 to a medium with index of refraction n2 as shown in the figure, the angle of incidence is greater than the angle of refraction.  Which one of the following statements is true?

(a)   n1 > n2
(b)   n1 < n2
(c)   The speed of light in medium 2 is greater than in medium 1.

### QUESTION 2*

This and the next question concern the same situation:

For this figure, if the angle of incidence in medium 1 is 30°, what is the angle α3 (with respect to the surface normal) of the light inside medium 3?

(a)   30°
(b)   45°
(c)   24.6°
(d)   36.4°
(e)   21.1°

### QUESTION 3*

For the geometry and refractive indices of the previous question, at the interface of medium 1 and 2 part of the light is reflected and  re-emerges in medium 1 at an angle α1.  What is the angle α1 (with respect to the surface normal) of this re-emerging light ray?

(a)   30°
(b)   45°
(c)   24.3°
(d)   36.4°
(e)   21.1°

### QUESTION 4**

A horizontally traveling light ray in air is incident on a prism made of glass with index of refraction 1.551 as shown in this figure.  The emerging angle from the prism is shown in the figure.

Assume now that the prism is replaced with another one of the same shape but with an index of refraction n = 1.663. With respect to the original prism, the emerging angle is

(a)   larger.
(b)   smaller.
(c)   equal.

### QUESTION 5*

A point source of light is in front of a flat mirror.  In the following figure, which point (A, B, or C) best represents the image of the object?

(a)
(b)
(c)

### QUESTION 6**

An object is placed in front of a convex mirror whose  radius of curvature is 25 cm.  A virtual image half the size of the object is formed.  At what distance is the object from the mirror?  (Note: the object position may not be drawn accurately)

(a)   25 cm
(b)   12.5 cm
(c)   6.25 cm
(d)   3.125 cm
(e)   50 cm

### QUESTION 7*

This and the next three questions concern the following situation:

A concave mirror has a radius of curvature of 5 m.  The object is initially placed at 2 m from the mirror (position A) .  Then the object is moved to Position B (6 m away from the mirror).  Is the size of the image of the object when it is placed at 6 m from the mirror larger, smaller or equal to the size of the image of the same object when it was placed at 2 m from the mirror?

(a)   larger
(b)   equal
(c)   smaller

### QUESTION 8*

The image when the object is 6 m from the mirror is inverted with respect to the image when the object is placed at 2 m from the mirror.

(T)   True
(F)   False

### QUESTION 9*

Calculate the magnification when the object is placed at 2 m from the mirror.

(a)   M = -1
(b)   M = -2
(c)   M = 2.5
(d)   M = 10
(e)   M = 5

### QUESTION 10*

The object is now placed at the center of the mirror (at a distance from the mirror equal to the radius of curvature). The magnification with respect to placing the object at position A (2 m from the mirror) is

(a)   larger.
(b)   smaller.
(c)   equal.

### QUESTION 11**

White light passes through the prism and comes out as shown below.  Which one of the statements below is wrong?
(a)   Red light gets deflected less than blue light.
(b)   The refractive index index is greater for red light than for blue light.
(c)   The refractive index of the prism depends on the wavelength of light.
(d)   The refractive index in  vacuum is independent of  the wavelength of light.
(e)   No dispersion will occur if the refractive index of the prism does not depend on the wavelength of light.

### QUESTION 12*

This and the next question concern the following situation:

A fiber optic line can transport light over long distances by using total internal reflection to reflect the light back into the fiber. The fiber shown has a core (n = 1.67) surrounded by a material of a different index (n = 1.33).

Inside the fiber, what is the maximum angle θcapture the light can have and still undergo total internal reflection?

(a)   θcapture = 31.8°
(b)   θcapture = 37.2°
(c)   θcapture = 43.4°
(d)   θcapture = 48.7°
(e)   θcapture = 54.3°

### QUESTION 13*

If the index of refraction of the cladding material is changed to 1.7, what will happen?

(a)   θcapture will increase.
(b)   θcapture will decrease.
(c)   Total internal reflection will no longer be possible for light traveling through the core of the fiber.

### QUESTION 14*

This and the next two questions concern the following situation:

Two lenses are separated by 18 cm.  Lens #1 is convergent and has a focal length of 5 cm Lens #2 is divergent  and has a focal length of -7 cm.  An object (arrow) is located 10 cm to the left of Lens #1.

If lens #2 were not present, the image formed by lens #1 would be

(a)   inverted relative to the object.
(b)   upright relative to the object.

### QUESTION 15**

Where is the final image of the pair of lenses?

(a)   to the left of lens #2 and more than 7 cm away from lens #2
(b)   to the right of lens #2 and more than 7 cm away from lens #2
(c)   to the left of lens #2 and less than 7cm away from lens #2
(d)   to the right of lens #2 and less than 7cm away from lens #2
(e)   infinity

### QUESTION 16*

The final image formed by the pair of lenses is

(a)   shorter than the object.
(b)   larger than object.
(c)   the same height as the object

### QUESTION 17*

This and the next question are about the following situation:

A farsighted student cannot see objects closer than 50 cm from his eyes. To correct his vision, he would need to see objects as close as 25 cm from his eyes (so that the lens should form a virtual image at 25 cm of an object at 50 cm).

What type of correction lens should he wear?

(a)   converging
(b)   diverging

### QUESTION 18*

What is the focal length of the needed lens?

(a)   50 cm
(b)   40 cm
(c)   30 cm
(d)   20 cm
(e)   10 cm

### QUESTION 19*

What is the magnification (m) for a converging lens with focal length f=4cm and an object placed at a distance p=10cm away from the lens? Note that m is negative if the image is inverted, and positive otherwise.

(a)   m = 0.667
(b)   m = 1.5
(c)   m= 1
(d)   m = -1.5
(e)   m = -0.667

### QUESTION 20**

Light of frequency f shines through a diffraction grating, producing a pattern of bright spots on a viewing screen as shown in the following figure. Note that the spots are 1 cm apart.

Later, a thick block of plastic with index of refraction n = 1.50 is placed between the diffraction grating and the screen, entirely filling the gap between the grating and the screen. After this is done, the separation between the bright spots on the screen is:

(a)   0.67 cm
(b)   1.00 cm
(c)   1.50 cm

### QUESTION 21*

The following graphs indicate the intensity of the diffraction pattern created by two different multiple-slit devices illuminated by light from identical lasers.

Which device has the larger number of slits?

(a)   device a
(b)   device b

### QUESTION 22*

Two loudspeakers are placed two meters apart as shown in the following figure. Initially, only one of the speakers is attached to a signal generator that produces a sinusoidal output voltage. A listener wanders about in front of the speakers, taking note of the intensity of sound in different locations. (The wavelength of the sound is 1m.)

Later, the second speaker is attached to the signal generator so that both speakers are driven in phase by the same signal. (The signal generator produces twice as much current in order to drive both speakers with the same amplitudes as the single speaker had been driven previously.) As the listener wanders through the same regions, he/she finds that the sound is

(a)   sometimes louder, sometimes softer than before.
(b)   always louder than before.
(c)   the same as before.

### QUESTION 23*

This and the next question are about the following situation:

A double-slit experiment is set up as shown in the following figure. Light from a laser illuminates a pair of slits etched in an opaque barrier. The spacing between the slits is 3 × 10-4 m; the distance from the barrier containing the slits to a viewing screen is 3 m. Because of diffraction, a pattern of light and dark spots is seen on the viewing screen. The distance from the central bright spot to the first bright spots on either side is 4 × 10-3 m.

What is the wavelength of the laser light illuminating the pair of slits?

(a)   2.00 × 10-6 nm
(b)   400 nm
(c)   500 nm
(d)   1.22 × 105 nm
(e)   107 nm

### QUESTION 24**

If the separation between the slits is increased by 50%, the spacing between the bright spots on the viewing screen will

(a)   increase by 100%.
(b)   increase by 50%.
(c)   remain unchanged.
(d)   decrease by 30%.
(e)   decrease by 50%.

### QUESTION 25*

Sunglasses sometimes use an anti-reflective coating on the back side of the lens to reduce the amount of stray light reflected into the eyes of the wearer from the back of the lens. An example of this is shown in the following figure, in which the thickness of the coating is t. Note the indices of refraction of the coating and the glass lens.

Stray light of wavelength λ = 560 nm is normally incident on the lens. In order to minimize reflections from the back of the lens, the thickness of the coating should be:

(a)   t = 1120 nm
(b)   t = 560 nm
(c)   t = 280 nm
(d)   t = 108 nm
(e)   t = 1.22 nm

### QUESTION 26**

Sunlight shines through a pinhole in an otherwise opaque window shade, creating a bright spot on a wall on the opposite side of the room. Because of diffraction effects, the color of the bright spot (as well as its intensity) varies with distance from the center of the spot. Assume that the range of wavelengths in sunlight extends from 400 nm (blue) to 700 nm (red).

Which one of the following statements can be correct?

Relative to the center of the bright spot, which is white,

(a)   point A contains equal intensities of all colors of light while point B consists only of red light.
(b)   point A contains only blue light while point B contains only red light.
(c)   points A and B only contain green light.
(d)   point A is deficient in blue light while point B is deficient in red light.
(e)   point A is deficient in red light while point B is deficient in blue light.

### QUESTION 27*

This and the next question are about the following situation:

A binary star system is 1018 meters (approximately 100 lightyears) from Earth. The two stars in the system move in circular orbits and remain a distance D apart. An earth-based telescope whose aperture is 2m observes light coming from the stars.

Assume that the starlight seen by the telescope has wavelength 500 × 10-9 m. What is the minimum distance D between the stars that will allow the telescope to resolve the binary system as comprising two well-separated stars?

(a)   2.50 × 10-7 m
(b)   3.00 × 108 m
(c)   3.05 × 1011 m
(d)   5.00 × 1011 m
(e)   5.00 × 1020 m

### QUESTION 28*

After astronomers modify the telescope's optical filters, observations of light from the binary star are performed at a wavelength of 400 × 10-9 m. How does the minimum resolvable distance D between the stars change?

(a)   D decreases by 20%
(b)   D remains unchanged
(c)   D increases by 20%

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.