### Fall 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 131. The exam period was 90 minutes; the mean score was 100.3; the median was 103. 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 electromagnetic microwave of wavelength 1.5 × 10-6 m travels in vacuum as shown below. The electric field has a maximum value of Emax = 80 N/C.

What is the frequency ν of the wave?

(a)   ν = 2 × 1014 Hz
(b)   ν = 7.5 × 106 Hz
(c)   ν = 250 Hz

### QUESTION 2*

This microwave impinges on a flat surface perpendicularly. What is the intensity I with which it hits the surface?

(a)   I = 3.2 × 10-6 W/m2
(b)   I = 6.5 × 10-4 W/m2
(c)   I = 9.7 × 10-2 W/m2
(d)   I = 8.5 W/m2
(e)   I = 1.7 × 102 W/m2

### QUESTION 3*

Which one of the following accurately describes features of the wave? (E and B refer to the values of the electric and magnetic fields, respectively.)

(a)   E and B constant in space, polarized along the z-direction
(b)   E and B varying in space in the same manner, polarized along the y-direction
(c)   traveling along the y-direction, E and B varying in space in the same manner
(d)   traveling along the y-direction, E and B constant in space
(e)   traveling along the z-direction, polarized along the y-direction

### QUESTION 4*

What is the magnetic field Brms carried by the wave?

(a)   Brms = 1.9 × 10-7 T
(b)   Brms = 6.2 × 10-3 T
(c)   Brms = 3.5 T

### QUESTION 5*

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

Consider a concave mirror having a focus f and center of curvature C as shown below. The mirror has a radius of curvature of R = 10 cm.

A real image is formed at a distance of 15 cm in front of the mirror. Where is the object placed for this image? The object is placed

(a)   3 cm behind the mirror.
(b)   7.5 cm behind the mirror.
(c)   3 cm in front of the mirror.
(d)   7.5 cm in front of the mirror.
(e)   10 cm in front of the mirror.

### QUESTION 6*

Where would you place an object in order to have the mirror form a virtual, enlarged image? The object would be placed

(a)   between the mirror and f.
(b)   between f and C.
(c)   just outside C.
(d)   very far away.
(e)   Such a situation could not exist.

### QUESTION 7*

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

A beam of blue light (λ = 400 nm) is incident on a pool of water (n = 1.33). There is a thin film of oil (n = 1.5) on top of the water. The light is incident normal to the surface. The angles are exaggerated for clarity.

What is the minimum thickness of the film which will result in constructive interference? You can assume that the gas above the film is air (n = 1.0).

(a)   66.7 nm
(b)   133.3 nm
(c)   153.8 nm
(d)   200.0 nm
(e)   400.0 nm

### QUESTION 8**

If you doubled the thickness of the oil film, you would see

(a)   constructive interference.
(b)   destructive interference.
(c)   neither.

### QUESTION 9*

An ant (5 mm in length) is sitting on a rock 50 m away from you. If the diameter of your pupil is 7 mm what is the longest wavelength λ which would resolve both ends of the ant?

(a)   λ = 321 nm
(b)   λ = 428 nm
(c)   λ = 573 nm
(d)   λ = 649 nm
(e)   λ = 725 nm

### QUESTION 10**

A man stands in front of a mirror. The mirror is on rollers and approaches him at a speed of 3 m/s relative to the ground. The speed vimage at which his image moves relative to himself is:

(a)   vimage = 3 m/s
(b)   vimage = 6 m/s
(c)   vimage = 13 m/s
(d)   vimage = 16 m/s
(e)   vimage = 23 m/s

### QUESTION 11**

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

An ultra-fast vehicle from outer space emits yellow light of wavelength λ = 556 nm. It comes to earth and passes you by at one-hundredth the speed of light (c/100).

Once the vehicle has passed you and is traveling away from you, the wavelength λ of light will appear to be

(a)   λ = 354 nm
(b)   λ = 562 nm
(c)   λ = 731 nm

### QUESTION 12**

After the object passes by, you remember that you are secretly a superhero. So, you take off after it at a fiftieth the speed of light (c/50). The wavelength λ' now appears:

(a)   λ' is shorter than λe.
(b)   λ' is longer than λe.
(c)   λ' is equal to λe.

### QUESTION 13*

A farsighted person wearing corrective lenses is looking at an object 25 cm away. His prescription lenses create an image of this object at his near point, 40 cm away. What is the power P of the prescription in diopters (m-1)?

(a)   P = -11.7
(b)   P = -5.00
(c)   P = +1.50
(d)   P = +5.00
(e)   P = +11.7

### QUESTION 14**

A ray of light strikes a window at angle θ = 50°, as shown in the diagram below. The window has thickness h = 3.50 mm, and is made of glass of refractive index n = 1.60 . What is the distance s by which the ray is displaced when it exits from the other side?

(a)   s = 1.41 mm
(b)   s = 1.54 mm
(c)   s = 1.91 mm
(d)   s = 3.21 mm
(e)   s = 7.98 mm

### QUESTION 15*

A dentist uses a small concave mirror to examine her patients' teeth. Suppose she holds the mirror a distance d = 1.20 cm from your tooth, and sees an upright image that is 3.5 times larger than the tooth. What is the focal length of the mirror that she is using? The focal length is

(a)   0.27 cm.
(b)   0.48 cm.
(c)   0.93 cm.
(d)   1.68 cm.
(e)   2.13 cm.

### QUESTION 16**

Consider two electromagnetic waves traveling in vacuum. One is a radio wave of wavelength 21 cm and the other, in the visual part of the spectrum, is of wavelength of 700 nm. What is the ratio vradio / vvisual of their velocities?

(a)   vradio / vvisual = 1.1 × 10-11
(b)   vradio / vvisual = 3.3 × 10-6
(c)   vradio / vvisual = 1
(d)   vradio / vvisual = 3.0 × 105
(e)   vradio / vvisual = 9.0 × 1010

### QUESTION 17***

Two radio towers, S1 with intensity 4 W/m2 and S2 with intensity 9 W/m2, are emitting coherent spherical radio waves. The two sources and the point P lie in the x-y plane as shown below. If the wavelength is 1 meter long what is the intensity I at point P? (Recall that IE2.)

(a)   I = 25 W/m2
(b)   I = 19 W/m2
(c)   I = 13 W/m2
(d)   I = 10 W/m2
(e)   I = 0 W/m2

### QUESTION 18*

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

An experimental physicist at UIUC measures the frequency of a laser by performing a double-slit experiment as shown above. She places a screen a distance L = 2 m away from the double slit. The slit separation is 0.35 mm. If she sees the first bright fringe at point P, 6.1 mm above central axis, what is the frequency of the laser? The frequency is:

(a)   1.2 × 1010 Hz
(b)   9.9 × 1012 Hz
(c)   2.8 × 1014 Hz
(d)   7.8 × 1014 Hz
(e)   9.1 × 1015 Hz

### QUESTION 19**

By mistake, her colleague drops the apparatus in a barrel of beer whose refractive index is n = 1.36. How would the interference patterns in the experiment change, if at all, when compared with when in air?

(a)   The bright fringes would be in the same places.
(b)   The bright fringes would move farther apart.
(c)   The bright fringes would move closer together.

### QUESTION 20**

Light of wavelength λ = 38 nm is incident on an array of evenly spaced molecules which form a diffraction grating, as shown. The spacing between the molecules is 235 nm.

What is the highest order diffraction fringe that can be observed?

(a)   m = 3
(b)   m = 6
(c)   m = 9
(d)   m = 12
(e)   The information is insufficient to determine the order.

### QUESTION 21**

A beam of white light is incident on a prism as shown in the figure below. The beam emerges from the prism into the colors of the rainbow, with red on top and green below.

Which statement on the index of refraction of the glass for red and green light is correct?

(a)   nred > ngreen
(b)   nred = ngreen
(c)   nred < ngreen

### QUESTION 22*

The index of refraction of the prism for blue light is nblue = 1.53. What must be the maximum angle θ of the prism for blue light to remain inside the prism by total internal reflection upon hitting the slanted edge?

(a)   θ = 38.2°
(b)   θ = 45.0°
(c)   θ = 49.2°
(d)   θ = 67.6°
(e)   θ = 77.8°

### QUESTION 23*

Two converging lenses are separated by a distance 12.5 cm. Lens 1 has a focal length f1 = 5 cm and lens 2 has a focal length f2 = 10 cm. An object is placed a distance 7.5 cm from lens 1.

Where is the image from lens 1 formed relative to its center?

(a)   3 cm
(b)   7.5 cm
(c)   10 cm
(d)   12 cm
(e)   15 cm

### QUESTION 24**

What is the magnification (ignoring sign) of the final image after lens 2?

(a)   0.78
(b)   1.60
(c)   3.57

### QUESTION 25**

The final image is

(a)   upright.
(b)   inverted.

### QUESTION 26*

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

Unpolarized light of intensity I0 is incident on two linear polarizers, as shown below. Polarizer 1 has a vertical transmission axis, and polarizer 2 has a transmission axis which makes an angle of 60° with the vertical.

What fraction of the intensity I0 is transmitted through the second polarizer?

(a)   Ifinal = 0.125 × I0
(b)   Ifinal = 0.25 × I0
(c)   Ifinal = 0.5 × I0
(d)   Ifinal = 0.75 × I0
(e)   Ifinal = I0

### QUESTION 27**

A third polarizer is inserted between polarizer 1 and 2. Polarizer 3 makes an angle of 30° with the vertical, as shown below. Compared to the previous situation, the transmitted light is

(a)   dimmer.
(b)   the same intensity.
(c)   brighter.

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.