Question 1

Which one of the following statements best explains why interference patterns are not usually observed for light from two ordinary light bulbs?

Accepted Answer

A) Diffraction effects predominate. 
B) The two sources are out of phase. 
C) The two sources are not coherent. 
D) The interference pattern is too small to observe. 
E) Light from ordinary light bulbs is not polarized. 
A) Diffraction effects predominate. 
B) The two sources are out of phase. 
C) The two sources are not coherent. 
D) The interference pattern is too small to observe. 
E) Light from ordinary light bulbs is not polarized. C

Question 2

A portion of a soap bubble appears yellow ($\lambda$ = 588.0 nm in vacuum) when viewed at normal incidence in white light. Determine the two smallest, non-zero thicknesses for the soap film if its index of refraction is 1.40.

Accepted Answer

A) 89 nm and 179 nm 
B) 89 nm and 268 nm 
C) 105 nm and 315 nm 
D) 125 nm and 375 nm. 
E) 170 nm and 536 nm 
A) 89 nm and 179 nm 
B) 89 nm and 268 nm 
C) 105 nm and 315 nm 
D) 125 nm and 375 nm. 
E) 170 nm and 536 nm C

Question 3

Light with a wavelength of 600.0 nm is incident on a single slit of width 6.5 $\mu$m. The resulting diffraction pattern is observed on a nearby screen and has a central maximum of width 3.5 m. What is the distance between the screen and the slit?

Accepted Answer

A) 9.5 m 
B) 19 m 
C) 38 m 
D) 57 m 
E) 76 m 
A) 9.5 m 
B) 19 m 
C) 38 m 
D) 57 m 
E) 76 m B

Question 4

The figure shows the interference pattern obtained in a double-slit experiment using light of wavelength 600 nm.
v  
-Which fringe results from a phase difference of 4$\pi$?

Accepted Answer

A) A 
B) B 
C) C 
D) D 
E) E 
A) A 
B) B 
C) C 
D) D 
E) E

Question 5

Which one of the following statements provides the most convincing evidence that electromagnetic waves have a transverse character?

Accepted Answer

A) Electromagnetic waves can be refracted. 
B) Electromagnetic waves can be reflected. 
C) Electromagnetic waves can be polarized. 
D) Electromagnetic waves can be diffracted. 
E) Electromagnetic waves exhibit interference. 
A) Electromagnetic waves can be refracted. 
B) Electromagnetic waves can be reflected. 
C) Electromagnetic waves can be polarized. 
D) Electromagnetic waves can be diffracted. 
E) Electromagnetic waves exhibit interference.

Question 6

Light from two sources, $\lambda$1 = 623 nm and $\lambda$2 = 488 nm, is incident on a diffraction grating that has 5550 lines/cm. What is the angular separation, $\theta$1 - $\theta$2, of the second order maxima of the two waves?

Accepted Answer

A) 11.0° 
B) 15.0° 
C) 25.0° 
D) 32.8° 
E) 43.8° 
A) 11.0° 
B) 15.0° 
C) 25.0° 
D) 32.8° 
E) 43.8°

Question 7

Two identical light waves, A and B, are emitted from different sources and meet at a point P. The distance from the source of A to the point P is LA; and the source of B is a distance LB from P. Which one of the following statements is necessarily true concerning the interference of the two waves?

Accepted Answer

A) A and B will interfere constructively because their amplitudes are the same. 
B) A and B will interfere constructively if LA = LB. 
C) A and B will interfere destructively if LA - LB = m$\lambda$ where m = 0, 1, 2, 3, ... 
D) A and B will interfere destructively if LA is not equal to LB. 
E) A and B will interfere constructively because their wavelengths are the same. 
A) A and B will interfere constructively because their amplitudes are the same. 
B) A and B will interfere constructively if LA = LB. 
C) A and B will interfere destructively if LA - LB = m$\lambda$ where m = 0, 1, 2, 3, ... 
D) A and B will interfere destructively if LA is not equal to LB. 
E) A and B will interfere constructively because their wavelengths are the same.

Question 8

Light is incident on two slits that are separated by 0.2 mm. The figure shows the resulting interference pattern observed on a screen 1.0 m from the slits. Determine the wavelength of light used in this experiment.

Accepted Answer

A) 0.05 nm 
B) 0.50 nm 
C) 50 nm 
D) 500 nm 
E) 5000 nm 
A) 0.05 nm 
B) 0.50 nm 
C) 50 nm 
D) 500 nm 
E) 5000 nm

Question 9

White light is passed through a diffraction grating that has 2.50 × 105 lines/m. On each side of the white central maximum, a spectrum of colors is observed. What is the wavelength of the light observed at an angle of 7.00° in the first-order bright fringes?

Accepted Answer

A) 487 nm 
B) 589 nm 
C) 632 nm 
D) 668 nm 
E) 731 nm 
A) 487 nm 
B) 589 nm 
C) 632 nm 
D) 668 nm 
E) 731 nm

Question 10

The figure shows the interference pattern obtained in a double-slit experiment using light of wavelength 600 nm.
v  
-Which one of the following phenomena would be observed if the distance between the slits is increased?

Accepted Answer

A) The fringes would become brighter. 
B) The central bright fringe would change position. 
C) The distance between dark fringes would increase. 
D) The distance between bright fringes would increase. 
E) The angular separation between the dark fringes would decrease. 
A) The fringes would become brighter. 
B) The central bright fringe would change position. 
C) The distance between dark fringes would increase. 
D) The distance between bright fringes would increase. 
E) The angular separation between the dark fringes would decrease.

Question 11

Light of wavelength 625 nm passes through a single slit of width 0.320 mm and forms a diffraction pattern on a flat screen located 8.00 m away. Determine the distance between the middle of the central bright fringe and the first dark fringe.

Accepted Answer

A) 0.156 cm 
B) 0.516 cm 
C) 1.56 cm 
D) 5.16 cm 
E) 6.51 cm 
A) 0.156 cm 
B) 0.516 cm 
C) 1.56 cm 
D) 5.16 cm 
E) 6.51 cm

Question 12

Two stars are just barely resolved by a telescope with a lens diameter of 0.500 m. Determine the angular separation of the two stars. Assume incident light of wavelength 500.0 nm.

Accepted Answer

A) 1.22 × 10-6 rad 
B) 5.66 × 10-5 rad 
C) 2.44 × 10-7 rad 
D) 4.88 × 10-5 rad 
E) 1.22 × 10-7 rad 
A) 1.22 × 10-6 rad 
B) 5.66 × 10-5 rad 
C) 2.44 × 10-7 rad 
D) 4.88 × 10-5 rad 
E) 1.22 × 10-7 rad

Question 13

Light with a wavelength of 644 nm uniformly illuminates a single slit. What is the width of the slit if the first-order dark fringe is located at $\theta$ = 0.125°?

Accepted Answer

A) 9.42 × 10-4 m 
B) 7.60 × 10-4 m 
C) 4.71 × 10-4 m 
D) 3.80 × 10-4 m 
E) 2.95 × 10-4 m 
A) 9.42 × 10-4 m 
B) 7.60 × 10-4 m 
C) 4.71 × 10-4 m 
D) 3.80 × 10-4 m 
E) 2.95 × 10-4 m

Question 14

Two candles are lit and separated by 0.10 m. If the diameter of the pupil of an observer's eye is 3.5 mm, what is the maximum distance that the candles can be away from the observer and be seen as two light sources? Use 545 nm for the wavelength of light in the eye.

Accepted Answer

A) 170 m 
B) 340 m 
C) 530 m 
D) 680 m 
E) 850 m 
A) 170 m 
B) 340 m 
C) 530 m 
D) 680 m 
E) 850 m

Question 15

The Hubble Space Telescope in orbit above the Earth has a 2.4 m circular aperture. The telescope has equipment for detecting ultraviolet light. What is the minimum angular separation between two objects that the Hubble Space Telescope can resolve in ultraviolet light of wavelength 95 nm?

Accepted Answer

A) 4.8 × 10-8 rad 
B) 7.0 × 10-8 rad 
C) 1.9 × 10-7 rad 
D) 1.5 × 10-7 rad 
E) 3.3 × 10-9 rad 
A) 4.8 × 10-8 rad 
B) 7.0 × 10-8 rad 
C) 1.9 × 10-7 rad 
D) 1.5 × 10-7 rad 
E) 3.3 × 10-9 rad

Question 16

A 30.0-mm wide diffraction grating produces a deviation of 30.0° in the second order principal maxima. The wavelength of light is 600.0 nm. What is the total number of slits on the grating?

Accepted Answer

A) 10 000 
B) 11 500 
C) 12 500 
D) 14 000 
E) 15 000 
A) 10 000 
B) 11 500 
C) 12 500 
D) 14 000 
E) 15 000

Question 17

The wavelength of light emitted from two distant objects is 715 nm. What is the minimum angle at which these objects can just be resolved when using binoculars with a 50-mm objective lens?

Accepted Answer

A) 10-2  degrees 
B) 10-3  degrees 
C) 10-4  degrees 
D) 10-5  degrees 
E) 10-6  degrees 
A) 10-2  degrees 
B) 10-3  degrees 
C) 10-4  degrees 
D) 10-5  degrees 
E) 10-6  degrees

Question 18

A double slit is illuminated with monochromatic light of wavelength 6.11 × 102 nm. The m = 0 and m = 1 bright fringes are separated by 1.8 cm on a screen which is located 3.5 m from the slits. What is the separation between the slits?

Accepted Answer

A) 4.0 × 10-5 m 
B) 8.0 × 10-5 m 
C) 1.2 × 10-4 m 
D) 1.6 × 10-4 m 
E) 2.4 × 10-4 m 
A) 4.0 × 10-5 m 
B) 8.0 × 10-5 m 
C) 1.2 × 10-4 m 
D) 1.6 × 10-4 m 
E) 2.4 × 10-4 m

Question 19

A lens that has an index of refraction of 1.61 is coated with a non-reflective coating that has an index of refraction of 1.45. Determine the minimum thickness for the film if it is to be non-reflecting for light of wavelength 5.60 × 102 nm.

Accepted Answer

A) 1.93 × 10-7 m 
B) 3.86 × 10-7 m 
C) 4.83 × 10-8 m 
D) 9.66 × 10-8 m 
E) 8.69 × 10-8 m 
A) 1.93 × 10-7 m 
B) 3.86 × 10-7 m 
C) 4.83 × 10-8 m 
D) 9.66 × 10-8 m 
E) 8.69 × 10-8 m

Question 20

What is the minimum (non-zero) thickness of a benzene (n = 1.501) thin film that will result in constructive interference when viewed at normal incidence and illuminated with orange light ($\lambda$vacuum = 615 nm)? A glass slide (ng = 1.620) supports the thin film.

Accepted Answer

A) 51.0 nm 
B) 306 nm 
C) 204 nm 
D) 102 nm 
E) 76.0 nm 
A) 51.0 nm 
B) 306 nm 
C) 204 nm 
D) 102 nm 
E) 76.0 nm

Exam 27: Interference and the Wave Nature of Light

Which one of the following statements best explains why interference patterns are not usually observed for light from two ordinary light bulbs?

A portion of a soap bubble appears yellow ( λ\lambdaλ = 588.0 nm in vacuum) when viewed at normal incidence in white light. Determine the two smallest, non-zero thicknesses for the soap film if its index of refraction is 1.40.

Light with a wavelength of 600.0 nm is incident on a single slit of width 6.5 μ\muμ m. The resulting diffraction pattern is observed on a nearby screen and has a central maximum of width 3.5 m. What is the distance between the screen and the slit?

The figure shows the interference pattern obtained in a double-slit experiment using light of wavelength 600 nm. v -Which fringe results from a phase difference of 4 π\piπ ?

Which one of the following statements provides the most convincing evidence that electromagnetic waves have a transverse character?

Light from two sources, λ\lambdaλ 1 = 623 nm and λ\lambdaλ 2 = 488 nm, is incident on a diffraction grating that has 5550 lines/cm. What is the angular separation, θ\thetaθ 1 - θ\thetaθ 2, of the second order maxima of the two waves?

Two identical light waves, A and B, are emitted from different sources and meet at a point P. The distance from the source of A to the point P is LA; and the source of B is a distance LB from P. Which one of the following statements is necessarily true concerning the interference of the two waves?

Light is incident on two slits that are separated by 0.2 mm. The figure shows the resulting interference pattern observed on a screen 1.0 m from the slits. Determine the wavelength of light used in this experiment.

White light is passed through a diffraction grating that has 2.50 × 105 lines/m. On each side of the white central maximum, a spectrum of colors is observed. What is the wavelength of the light observed at an angle of 7.00° in the first-order bright fringes?

The figure shows the interference pattern obtained in a double-slit experiment using light of wavelength 600 nm. v -Which one of the following phenomena would be observed if the distance between the slits is increased?

Light of wavelength 625 nm passes through a single slit of width 0.320 mm and forms a diffraction pattern on a flat screen located 8.00 m away. Determine the distance between the middle of the central bright fringe and the first dark fringe.

Two stars are just barely resolved by a telescope with a lens diameter of 0.500 m. Determine the angular separation of the two stars. Assume incident light of wavelength 500.0 nm.

Light with a wavelength of 644 nm uniformly illuminates a single slit. What is the width of the slit if the first-order dark fringe is located at θ\thetaθ = 0.125°?

Two candles are lit and separated by 0.10 m. If the diameter of the pupil of an observer's eye is 3.5 mm, what is the maximum distance that the candles can be away from the observer and be seen as two light sources? Use 545 nm for the wavelength of light in the eye.

The Hubble Space Telescope in orbit above the Earth has a 2.4 m circular aperture. The telescope has equipment for detecting ultraviolet light. What is the minimum angular separation between two objects that the Hubble Space Telescope can resolve in ultraviolet light of wavelength 95 nm?

A 30.0-mm wide diffraction grating produces a deviation of 30.0° in the second order principal maxima. The wavelength of light is 600.0 nm. What is the total number of slits on the grating?

The wavelength of light emitted from two distant objects is 715 nm. What is the minimum angle at which these objects can just be resolved when using binoculars with a 50-mm objective lens?

A double slit is illuminated with monochromatic light of wavelength 6.11 × 102 nm. The m = 0 and m = 1 bright fringes are separated by 1.8 cm on a screen which is located 3.5 m from the slits. What is the separation between the slits?

A lens that has an index of refraction of 1.61 is coated with a non-reflective coating that has an index of refraction of 1.45. Determine the minimum thickness for the film if it is to be non-reflecting for light of wavelength 5.60 × 102 nm.

What is the minimum (non-zero) thickness of a benzene (n = 1.501) thin film that will result in constructive interference when viewed at normal incidence and illuminated with orange light ( λ\lambdaλ vacuum = 615 nm)? A glass slide (ng = 1.620) supports the thin film.

Introduction and Mathematical Concepts

Kinematics in One Dimension

Kinematics in Two Dimensions

Forces and Newtons Laws of Motion

Dynamics of Uniform Circular Motion

Work and Energy

Impulse and Momentum

Rotational Kinematics

Rotational Dynamics

Simple Harmonic Motion and Elasticity

Fluids

Temperature and Heat

The Transfer of Heat

The Ideal Gas Law and Kinetic Theory

Thermodynamics

Waves and Sound

The Principle of Linear Superposition and Interference Phenomena

Electric Forces and Electric Fields

Electric Potential Energy and the Electric Potential

Electric Circuits

Magnetic Forces and Magnetic Fields

Electromagnetic Induction

Alternating Current Circuits

Electromagnetic Waves

The Refl Ection of Light: Mirrors

The Refraction of Light: Lenses and Optical Instruments

Special Relativity

Particles and Waves

The Nature of the Atom

Nuclear Physics and Radioactivity

Ionizing Radiation, Nuclear Energy, and Elementary Particles

Filters

A portion of a soap bubble appears yellow ( $\lambda$ = 588.0 nm in vacuum) when viewed at normal incidence in white light. Determine the two smallest, non-zero thicknesses for the soap film if its index of refraction is 1.40.

Light with a wavelength of 600.0 nm is incident on a single slit of width 6.5 $\mu$ m. The resulting diffraction pattern is observed on a nearby screen and has a central maximum of width 3.5 m. What is the distance between the screen and the slit?

Light from two sources, $\lambda$ ₁ = 623 nm and $\lambda$ ₂ = 488 nm, is incident on a diffraction grating that has 5550 lines/cm. What is the angular separation, $\theta$ ₁ - $\theta$ ₂, of the second order maxima of the two waves?

White light is passed through a diffraction grating that has 2.50 × 10⁵ lines/m. On each side of the white central maximum, a spectrum of colors is observed. What is the wavelength of the light observed at an angle of 7.00° in the first-order bright fringes?

Light with a wavelength of 644 nm uniformly illuminates a single slit. What is the width of the slit if the first-order dark fringe is located at $\theta$ = 0.125°?

A double slit is illuminated with monochromatic light of wavelength 6.11 × 10²nm. The m = 0 and m = 1 bright fringes are separated by 1.8 cm on a screen which is located 3.5 m from the slits. What is the separation between the slits?

A lens that has an index of refraction of 1.61 is coated with a non-reflective coating that has an index of refraction of 1.45. Determine the minimum thickness for the film if it is to be non-reflecting for light of wavelength 5.60 × 10²nm.

What is the minimum (non-zero) thickness of a benzene (n = 1.501) thin film that will result in constructive interference when viewed at normal incidence and illuminated with orange light ( $\lambda$ _vacuum = 615 nm)? A glass slide (n_g = 1.620) supports the thin film.