P214Exam Form A

PHYSICS 214 - Midterm Exam Fall 2007

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This exam is worth 100 points. It consists of 20 multiple-choice questions worth 5 points each. Indicate your answers to the multiple-choice questions in the appropriate spaces on the answer sheet. Choose the best answer for each question from among the choices provided. Don't get hung up on the questions. They should only take a few minutes each. If you find yourself spending more than a few minutes on a question you are probably looking at it the wrong way. You should skip it for now and come back to it later.

Enter your student number on the scantron sheet prior to answering the first question. You will not be given time at the end of the exam to do so.

Do not begin the examination until you are instructed to do so.

GOOD LUCK

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1. Monochromatic light, at normal incidence, strikes a thin film in air. If λ denotes the wavelength inthe film, what is the thinnest film in which the reflected light will be a maximum?

A. much less than λB. λ/4C. λ/2D. 3λ/4E. λ

2. Two slits in an opaque barrier each have a width of 0.020 mm and are separated by 0.050 mm.When coherent monochromatic light passes through the slits the number of interference maximawithin the central diffraction maximum:

A. is 1.B. is 2.C. is 4.D. is 5.E. cannot be determined unless the wavelength is given.

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3. Two wavelengths, 800 nm and 600 nm, are used separately in single-slit diffraction experiments.The diagram shows the intensities on a far-away viewing screen as function of the angle made bythe rays with the straight-ahead direction. If both wavelengths are then used simultaneously, atwhich angle is the light on the screen purely 800-nm light?

A. AB. BC. CD. DE. E

4. 600-nm light is incident on a diffraction grating with a ruling separation of 1.7 × 10-6 m. Thesecond order line occurs at a diffraction angle of:

A. 0B. 10°C. 21°D. 42°E. 45°

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5. An erect object placed outside the focal point of a converging lens will produce an image that is:

A. erect and virtual.B. inverted and virtual.C. erect and real.D. inverted and real.E. impossible to locate.

6. A spherical concave mirror forms a real image at 15 cm when the object is at 30 cm. What is theradius of curvature of the mirror?

A. 30 cmB. 20 cmC. 15 cmD. 12.5 cmE. 10 cm

7. A minimum in a single slit diffraction pattern occurs because:

A. every light wave from the slit interferes constructively with some other light wave from theslit.

B. every light wave from the slit interferes destructively with some other light wave from the slit.C. the light waves from the top and bottom edge of the slit interfere destructively with one

another.D. light from every point in the slit interferes constructively with light from every other point in

the slit.E. light from every point in the slit interferes destructively with light from every other point in the

slit.

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8. One of the two slits in a Young's double slit experiment is painted over so that it transmits onlyone-half the intensity of the other slit. As a result:

A. the dark fringes get brighter and the bright ones get darker.B. the fringe system disappears.C. the bright fringes get brighter and the dark ones get darker.D. the bright fringes get dimmer and the dark fringes do not change.E. just the dark fringes just get brighter.

9. When light travels from medium X to medium Y as shown:

A. both the speed and the frequency decrease.B. both the speed and the frequency increase.C. both the speed and the wavelength decrease.D. both the speed and the wavelength increase.E. both the wavelength and the frequency are unchanged.

10. Consider two sets of perfect polarizing sheets: (A) three polaroids, each rotated 45° with respectto the previous one; and (B) four polaroids, each rotated 30° with respect to the previous one.Which combination transmits more light when each set is separately illuminated with unpolarizedlight?

A. AB. BC. A = B, because no light gets throughD. A = B, and light gets through bothE. not enough information is given

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11. Two coherent electromagnetic waves are incident simultaneously at some point in space. Theintensity of each independent wave is I0. What is the intensity of the superposition of these twowaves if the phase difference is 2π?

A. 4I0B. 2I0C. I0D. zeroE. I0/4

12. Consider (I) the law of reflection and (II) the law of refraction. Huygens’ principle can be used toderive:

A. only I.B. only II.C. both I and II.D. neither I nor II.E. the question is meaningless because Huygens’ principle is for wave fronts whereas both I

and II concern rays.

13. Microwaves differ from visible light waves in that microwaves

A. travel slowerB. have a longer wavelengthC. travel fasterD. have a shorter wavelengthE. can only exist in a physical medium

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14. A plane electromagnetic wave is traveling in the positive z direction and has polarization (electricfield) vector pointing in the positive y direction. The magnetic field vector points:

A. in the positive y direction.B. in the negative y direction.C. in the positive x direction.D. in the negative x direction.E. in the negative z direction.

15. In a Young's double-slit experiment, light of wavelength 500 nm illuminates two slits which areseparated by 1 mm. The separation between adjacent bright fringes on a screen 5 m from theslits is:

A. 0.10 cmB. 0.25 cmC. 0.50 cmD. 1.0 cmE. none of the above

16. In the problem of single slit diffraction, phasors can be added up to represent contributions fromdifferent elements of the slit. Rank the net intensity of the following four cases:

a) the phasors from a straight line.b) the phasors form a complete circle.c) the phasors form a semi-circle.d) the phasors form two complete circles.

A. a > c > (d = b)B. a > c > b > dC. d > b > c > aD. c > (a = d) > bE. a > (d = b) > c

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17. A card marked IAHIO8 is standing upright in front of a plane mirror. Which of the following isNOT true?

A. The image is virtual.B. The image shifts its position as the observer shifts his position.C. The image appears as 8OIHAI to a person looking in the mirror.D. The image is caused mostly by specular rather than diffuse reflection.E. The image is the same size as the object.

18. A point source emits electromagnetic energy isotropically at a rate of 100 W. The intensity 10 mfrom the source is:

A. 10 W/m2

B. 1.6 W/m2

C. 1 W/m2

D. 0.024 W/m2

E. 0.080 W/m2

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19. The light waves represented by the three rays shown in the diagram all have the same frequency.4.7 wavelengths fit into layer 1, 3.2 wavelengths fit into layer 2, and 5.3 wavelengths fit intolayer 3. Rank the layers according to the speeds of the waves, least to greatest.

A. 1, 2, 3B. 2, 1, 3C. 3, 2, 1D. 3, 1, 2E. 1, 3, 2

20. Light of wavelength 632 nm is incident upon a sapphire (n = 1.77) prism at an angle of incidence(with respect to the normal) of 70°. If the angle of the prism is 60°, the angle of refraction at thesecond face, θ, is:

A. 26°B. 37°C. 56°D. 63°E. 70°

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Some useful constants and formulae Speed of light 82.9979 10 /c m s= × Gravitational constant 11 2 26.67 10 /G N m kg−= × ⋅

Permittivity constant 120 8.85 10 /F mε −= × Permeability constant 6

0 1.26 10 /H mμ −= × Near point PN = 25 cm Planck’s constant h = 6.63 x 10-34 J.s = 4.14 x 10-15 eV.s e = 1.60 x 10-19 C atomic mass m(11H) =1.007825 u me = 9.11 x 10-31 kg = 0.000549 u 1 u = 1.6605 x 10-27 kg = 931.5 MeV/c2 mp = 1.6726 x 10-27 kg = 1.00728 u 1eV = 1.602 x 10-19 J mN = 1.6749 x 10-27 kg = 1.008665 u 1240 hc eV nm= ⋅ Transverse Waves:

( , ) sin( )my x t y kx tω= − 2k πλ

= 2 2 fTπω π= = v f

T kλ ωλ= = =

Electromagnetic Waves:

( , ) sin( )mE x t E kx tω= − ( , ) sin( )mB x t B kx tω= − m

m

E cB

=

2m

rmsEE =

0 0

1cε μ

= 0

1S E Bμ

= ×r r r

2

0 0

1 1S EB Ecμ μ

= = 2

0

1rmsI E

cμ= 24

sourcePIrπ

=

Unpolarized Light: 012

I I= Fully Polarized Light: 20 cosI I θ=

Law of reflection 1 1'θ θ= Snell’s Law 1 1 2 2sin sinn nθ θ=

Total internal reflection 1 2

1

sincnn

θ −= Brewster angle 1 2

1

tanBnn

θ −=

Total Absorption cIpc

= Total Reflection 2

rIp

c=

Mirrors and Lenses:

Spherical Mirrors/Thin Lenses: 1 1 1p i f+ =

imp

= −

Spherical Mirrors: 2rf =

Refracting Surface: 1 2 2 1n n n np i r

−+ = 2

1

ni pn

= −

cnv

= n nλλ = ( )2 1

2 L n nπλ

Δ = −φ 2 LπλΔ

Δ =φ

magnifier mθ = PN/f

microscope m = - [l PN]/fobfey

telescope m = - fob/fey

Constructive Interference: sin , 0,1,2,... L d m mθ λΔ = = =

Destructive Interference: 1sin2

L d mθ λ⎛ ⎞Δ = = +⎜ ⎟⎝ ⎠

0, 1, 2,...m =

Intensity in double-slit interference 204 cos

2I I=

φ

2 sindπ θλ

=φ

Interference from thin films: Maxima: 2

122

L mnλ⎛ ⎞= +⎜ ⎟

⎝ ⎠ Minima:

2

2L mnλ

=

Single-slit Diffraction:

Minima sina mθ λ= Intensity 2sin( ) , where sin

2maI I α φ πθ α θ

α λ⎛ ⎞= = =⎜ ⎟⎝ ⎠

Resolvability: Resolving angle θ = 1.22λ/a circular aperture θ = 1.22λ/D Resolving power RP = θ L

Resolving power for microscope (telescope) RP = 1.22 λf/D Double-slit Diffraction:

22 sin( ) (cos ) , where sin and sinm

a dI I α π πθ β α θ β θα λ λ

⎛ ⎞= = =⎜ ⎟⎝ ⎠

Maxima lines sind mθ λ=

Diffraction gratings:

Half-width of line coshw Ndλθ

θΔ =

Answer Key for Test "P214Mt1Fa07.tst", 11/7/2007No. in

Q-BankNo. onTest Correct Answer

35.Sec07 18 1 B36.Sec07 9 2 D36.Sec05 19 3 C36.Sec08 8 4 E34.Sec07 42 5 D34.Sec05 5 6 B36.Sec03 6 7 B35.Sec04 5 8 A33.Sec08 22 9 C33.Sec07 8 10 B35.Sec06 1 11 A35.Sec02 6 12 C33.Sec02 10 13 B33.Sec03 3 14 D35.Sec04 17 15 B36.Sec04 5 16 A34.Sec03 11 17 B33.Sec05 11 18 E35.Sec02 7 19 D33.Sec08 6 20 C

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