SparkNotes: Review of Optics: Multiple Choice Test on Optics

1. The quantity

is equal to:

(A) The magnitude of the electric field of an electromagnetic wave.

(B) The speed of light in vacuum.

(C) The index of refraction of a medium.

(D) The dielectric constant of a medium.

2. One reason why the sky appears blue is because:

(A) Much more red light than blue light is absorbed by air atoms.

(B) Red light is reflected by the atmosphere.

(C) Blue light is scattered to a greater extent than red light.

(D) Higher energy light waves have more penetration through the atmosphere.

3. If φ₁ and phi₂ are solutions to the wave equation, which of the following is not also a solution, if a and b are real constants.

(A) aφ₁ + b

(B) a²bφ₂

(C) - φ₁.

(D) aφ₁φ₂

4. The direction of propagation of an electromagnetic wave is the same as:

(A) E

(B) E.B

(C) E×B

(D) B×E

5. Photons always propagate with speed c, but light appears to travel at a speed different from c in dense media. How can we account for this phenomenon?

(A) Propagation in media depends on re-radiation by electron-oscillators, which takes a finite time to occur.

(B) Electron oscillators in the medium introduce a phase change upon re-radiation.

(C) A medium is a different reference frame to vacuum, so the difference in the observed speed of light is a consequence of relativity.

(D) Light is slowed down because it does not take a straight line path through the dense medium.

6. Which of the following is true: I) A reflected beam always has the same irradiance as the incident beam; II) a reflected beam lies in the same plane as the incident beam; III) a reflected beam always makes an angle θ = sin^-1(n_t/n_i) with the normal to the interface.

(A) I only.

(B) I and II.

(C) II and III.

(D) II only.

7. The irradiance of a light ray is proportional to:

(A) The frequency of the light ray.

(B) The frequency of the light ray squared.

(C) The amplitude of the electric field of the light ray.

(D) The amplitude of the electric field of the light ray squared.

8. The phase velocity of the wave described by ψ = A sin(kx + ωt + π/2) is:

(A) x/t

(B) ω/k

(C) A/ω

(D) π/2k

9. The period of the wave described by ψ = A cos(kx + ωt + π) is:

(A) 2π/ω

(B) ω/k

(C) ω/π

(D) 1/ω

10. If we have electric and magnetic fields given by:

E = E₀cos(kz - ωt)
B = B₀cos(kz - ωt)

In SI units, what conditions need to be satisfied if these fields are to satisfy Maxwell's equations?

(A) E₀ = B₀ and ω = c

(B) E₀ = c and B₀ = ω/k

(C) E₀ = ω/k and B₀ = c

(D) ω/k = c and E₀ = cB₀.

11. Which of the following functions of space and time defines a wave with speed v in the negative x direction?

(A) f (x - vt)

(B) f (x + vt)

(C) f (vt - x)

(D) f (vx - t)

12. The profile of a wave with equation ψ(x, t) =

is equal to:

(A)

(B)

(C)

(D)

13. Maxwell's equations: I) predict the speed of an electromagnetic wave to be μ₀ε₀; II) imply that an electric field changing in time will produce a magnetic field; III) impose boundary conditions that must be satisfied at an interface between two media.

(A) All of these are true.

(B) I and II are true, but not III.

(C) II and III are true, but not I.

(D) II is true, but not I or III.

14. Which of the following is correct:

(A) Sound waves and waves on strings are transverse, but light is longitudinal.

(B) Light and sound waves are transverse, but waves on strings are longitudinal.

(C) Light waves are transverse, sound waves and waves on strings are longitudinal.

(D) None of these.

15. The wavelength of a photon with an energy of 3.6 eV is:

(A) 869 nanomters.

(B) 345 nanometers

(C) 543 nanometers

(D) 552 nanometers.

16. Which of the following would not be a good description of a photon:

(A) Light particles that cannot transport energy or momentum.

(B) The quanta of the electromagnetic field.

(C) Massless particles carrying the energy of radiation.

(D) Entities that always travel at c.

17. A photon has a chance of being absorbed by an atom, only if:

(A) It strikes it at exactly the right place.

(B) It has the same frequency as the natural frequency at which electrons in the atom like to vibrate.

(C) It has the exact energy corresponding to a quantum energy jump.

(D) Its wavelength is approximately equal to the width of the atom.

18. Fermat's principle states that:

(A) The path taken by a light ray is always the shortest.

(B) The path taken by a light ray is the one for which the optical path length is a maximum.

(C) The path a light ray takes maximizes its time of travel between any two points.

(D) The path taken by a light ray always minimizes the time between any two points.

19. Light behaves in accordance with Fermat's principle because:

(A) This is the only way in which energy can be conserved.

(B) Light along all alternate paths effectively cancels out due to interference.

(C) In order to propagate with speed c, light must take the shortest route through spacetime.

(D) None of these.

20. The Fresnel Equations: I) are a consequence of Maxwell's equations; II) imply a phase shift of 180^o when light in vacuum with electric field perpendicular to the plane of incidence reflects from a surface; III) imply that polarization can be achi eved by reflection.

(A) I, II and III are all true.

(B) Only I and II are true.

(C) Only I and III are true.

(D) Only I is true.

21. Total internal reflection can occur:

(A) Only when the incident medium is less dense than the transmitting medium.

(B) Only when the incident medium is denser than the transmitting medium.

(C) Only when the media are of approximately equal density.

(D) Irrespective of the density of the media.

22. The critical angle for an air-water interface (the index of refraction of water is n = 1.33) is about:

(A) 48.8^o

(B) 42.2^o

(C) 31.6^o

(D) 58.4^o.

23. The spectrum observed when white light is shone through a prism is best explained by:

(A) Diffraction

(B) Dichroism

(C) Distortion

(D) Dispersion

24. For a substance with natural frequencies in the infra-red range the color that will exhibit a higher index of refraction, and the type of dispersion are respectively:

(A) red, normal.

(B) red, anomalous

(C) blue, normal

(D) blue, anomalous

25. An expression for the absolute index of refraction is:

(A) v/c

(B) c/

(C) c

(D)

26. A light wave in air enters a substance in which light travels at 2.64×10⁸ m/s at an angle of 48^o to the surface. The angle of refraction is:

(A) 36.1^o

(B) 49.5^o

(C) 57.6^o

(D) 40.8^o

27. Which of the following is a correct expression for the relative amplitude of a reflected ray (electric field perpendicular to the incident plane)?

(A) r_⊥ =

(B) r_⊥ =

(C) r_⊥ =

(D) r_⊥ =

28. Images formed by a convex mirror are:

(A) Always enlarged.

(B) Always farther from the mirror than the focus.

(C) Always real.

(D) Always upright.

29. For a concave mirror of focal length 5 centimeters, the image of an object placed 7 centimeters from the mirror will be:

(A) Real, inverted and magnified.

(B) Real, upright and magnified.

(C) Virtual, upright and diminished.

(D) Virtual, inverted and magnfied.

30. A convex lens has a focal length of 3 centimeters. How far from the mirror is the object, if the image formed is 4 centimeters away?

(A) 10 centimeters.

(B) 12 centimeters.

(C) 7 centimeters.

(D) 1 centimeter.

31. What is the focal length of a plano-convex (planar on one side and convex on the other) lens made of glass with index of refraction n = 1.40 and with the curved side having a radius of curvature of 20 centimeters?

(A) 0.02 centimeters.

(B) 0.07 centimeters.

(C) 14.3 centimeters.

(D) 50 centimeters.

32. What is the magnification of an image formed by an object 10 centimeters distant from a concave mirror of focal length 2 centimeters.

(A) 25

(B) -25

(C) 1/25

(D) -1/25

33. Concave mirrors can suffer from:

(A) Chromatic aberration but not spherical aberration.

(B) Spherical aberration but not chromatic aberration.

(C) Neither spherical nor chromatic aberration.

(D) Both spherical and chromatic aberration.

34. Concave lenses can suffer from:

(A) Chromatic aberration but not spherical aberration.

(B) Spherical aberration but not chromatic aberration.

(C) Neither spherical nor chromatic aberration.

(D) Both spherical and chromatic aberration.

35. Virtual images are so called because:

(A) Light rays that form the image only appear to come from the position where the image is.

(B) The image is too small to be seen with the naked eye.

(C) The image can only be projected onto a screen.

(D) The image is located behind the lens or mirror.

36. To form a diminished image with a convex lens, the object must be placed:

(A) Less than one focal length from the mirror.

(B) Exactly at the focus.

(C) Between one and two focal lengths away.

(D) Further than 2 focal lengths away.

37. The radius of curvature of a convex mirror of focal length -8 centimeters is:

(A) -4 centimeters.

(B) 16 centimeters.

(C) 4 centimeters.

(D) -16 centimeters.

38. All images formed by diverging lenses are:

(A) Virtual, inverted and enlarged.

(B) Real, inverted and diminished.

(C) Virtual, upright and diminished.

(D) Real, upright and enlarged.

39. Which of the following is true for all lenses:

(A) All magnified images are inverted.

(B) All virtual images are inverted.

(C) All real images are inverted.

(D) All diminished images are inverted.

40. If x_i is the distance between the image and the focal point on the same side of the lens (for a convex lens), an alternate expression for the transverse magnification is:

(A) -

(B)

(C)

(D) -

41. Which of the following is not a consequence of interference effects?

(A) Diffraction

(B) The bright and dark fringes observed by Young in 1803.

(C) The variety of colors reflected from thin soap films.

(D) Polarization

42. In Young's Double Slit Experiment, increasing the wavelength of light will serve to:

(A) Increase the separation between the fringes and increase their width.

(B) Increase the separation between the fringes, but decrease their width.

(C) Decrease the separation between the fringes and decrease their width.

(D) Decrease the separation between the fringes, but increase their width.

43. In a Young's Double Slit interference pattern, the fourth maximum has an irradiance that is roughly:

(A) As bright as the central maximum.

(B) Half as bright as the central maximum.

(C) 8% as bring as the central maximum.

(D) 0.08% as bright as the central maximum.

44. If the finite width of the slits was taken into account, one would expect the fourth maximum of the double slit interference pattern to be:

(A) Brighter than when the slits are assumed to be infinitesimally thin.

(B) Less bright than when the slits are assumed to be infinitesimally thin.

(C) About the same brightness as when the slits are assumed to be infinitesimally thin.

(D) More or less bright, depending on the width of the slits and the wavelength of the light used.

45. For a single slit, light is heading in a direction such that rays from a point source in the middle of the slit travels exactly λ farther than light at the very edge of the slit. The point at which this light arrives on a distant screen will be:

(A) A bright fringe.

(B) Half way between a bright fringe and a dark fringe.

(C) A point where I = 1/3I₀.

(D) A dark fringe.

46. If β =

, the zeroes of irradiance for a single slit occur when:

(A) β = ±nπ/2 for n an odd integer.

(B) β = ±nπ for n any integer.

(C) β = ±2nπ for n any integer.

(D) β = tanβ (±1.4303π, ±2.4590π, ±3.4707π, etc.)

47. Light reflecting from a dense medium is:

(A) Partially polarized is the plane perpendicular to the surface.

(B) Partially polarized in the plane parallel to the plane of incidence.

(C) Partially polarized in the plane perpendicular to the incident plane.

(D) None of these.

48. Randomly polarized light moving along the x axis in the positive x-direction is incident on an atomic oscillator at the origin. If you are at the point (0, y₀, 0), you will observe:

(A) Light with an electric field oscillating in the x direction.

(B) Light with an electric field oscillating in the y direction.

(C) Light with an electric field oscillating in the z direction.

(D) Unpolarized light.

49. A birefringent material is best described as:

(A) Having two different transmission axes.

(B) Having atoms with two different resonant frequecies.

(C) Circularly polarizing natural light.

(D) Having two different indices of refraction.

50. Light is propagating is a direction directly away from you, with an electric field that appears to be rotating in its orientation in the counterclockwise direction. The polarization state of such a wave is:

(A) Randomly polarized.

(B) Plane polarized.

(C) Left-circularly polarized.

(D) Right-circularly polarized.