Module 32: Interference and Diffraction

Monochromatic light of wavelength lambda is equal to 500 nanometers is directed through two narrow parallel slits that are separated by 5 micrometers. There is a viewing screen 1.5 m away from the slits that is used to observe the interference pattern that emerges from the light shining through the slits. The interference pattern is a series of alternating, equally spaced, bright and dark fringes, like that shown in the figure. What is the distance from the central bright fringe to the 3rd order minimum?

.38 m

Using a green laser with a 500 nm wavelength, you shine light through a narrow slit and onto a screen that is 5 m away from the slit. You then observe a diffraction pattern like that shown in the figure. If you measure the width of the central bright fringe to be 50 mm, what is the width of the slit?

0.1 mm

Monochromatic light of wavelength lambda is equal to 500 nanometers is directed through two narrow parallel slits that are separated by 5 micrometers. There is a viewing screen 1.5 m away from the slits that is used to observe the interference pattern that emerges from the light shining through the slits. The interference pattern is a series of alternating, equally spaced, bright and dark fringes, like that shown in the figure. What is the distance from the central bright fringe to the 3rd order maximum?

0.45 m

A diffraction grating with 1000 lines per mm is used in a spectrometer to measure the wavelengths of light emitted from a gas discharge tube. What is the wavelength of the first order maximum if the diffraction angle measured is 30°?

0.5 µη

If there are 600 lines per mm on a diffraction grating, what is the distance between adjacent slits?

1.67 x 10*-6 m

A very thin non-reflective coating is applied to glass to reduce the amount of 550-nm wavelength light that is reflected. The refractive index of the coating is 1.3 and the refractive index of the glass is 1.5. What is the thinnest layer of coating that can be used to result in the destructive interference of reflected light with a 550 nm wavelength?

106 nm

A thin reflective coating is applied to glass to increase the amount of infrared (IR) light that is reflected from the glass. The refractive index of the coating is 1.7 and the refractive index of the glass is 1.5. What is the thinnest layer of coating that will result in the constructive interference of reflected infrared light with wavelength of 800 nm?

118 nm

Light propagating in a material with index of refraction n1 is incident on a new material with index of refraction n2 > n1. An example of this could be light initially traveling through air and reflecting at an air-water boundary. Some of the incident light reflects at this boundary between materials 1 and 2 and continues to propagate in material 1. How does the phase of the reflected light compare to the phase of the incident light?

118 nm

Using a green laser with a 500 nm wavelength, you shine light through a narrow slit of width 20 micrometers and onto a screen that is 5 m away from the slit. You then observe a diffraction pattern like that shown in the figure. What is the distance from the center of the pattern to the 3rd order dark fringe?

37.5 cm

You shine monochromatic light of wavelength lambda through a narrow slit of width a is approximately equal to lambda and onto a screen that is very far away from the slit. What do you observe on the screen?

A series of bright and dark fringes with the central bright fringe being wider and brighter than the other bright fringes

You shine monochromatic light of wavelength lambda through a narrow slit of width a is much greater than lambda and onto a screen that is very far away from the slit. What do you observe on the screen?

One bright band

Monochromatic light of wavelength lambda, such as light from a laser, is directed through two narrow parallel slits that are a distance d apart. There is a viewing screen a very long distance R away from the slits that is used to observe the interference pattern that emerges from the light shining through the slits. The interference pattern is a series of alternating, equally spaced, bright and dark fringes, like that shown in the figure. If you replaced the pair of slits of slit spacing d with a new pair of slits that have a spacing d' > d, how is the new interference pattern different from the original one?

The bright and dark fringes are closer together.

Monochromatic light of wavelength lambda, such as light from a laser, is directed through two narrow parallel slits that are a distance d apart. There is a viewing screen a very long distance R away from the slits that is used to observe the interference pattern that emerges from the light shining through the slits. The interference pattern is a series of alternating, equally spaced, bright and dark fringes, like that shown in the figure. If you submerged the entire apparatus into a tank of water, how is the new interference pattern different from the original one?

The bright and dark fringes are closer together.

Using a green laser with a 500 nm wavelength, you shine light through a narrow slit and onto a screen that is 5 m away from the slit. You then observe a diffraction pattern like that shown in the figure. If you replace the slit with one that is narrower, what happens to the central bright fringe?

The central bright fringe gets wider.

A diffraction grating with 1000 lines per mm is used in a spectrometer to measure the wavelengths of light emitted from a gas discharge tube. You measure the diffraction angle to be at 20° for one emission line. What would happen to this emission line's diffraction angle if you replaced the diffraction grating with one having 500 lines per mm instead?

The diffraction angle would be less than 20°

A monochromatic light source is directed past a straight edge (like a razor blade) and onto a screen. Why does the shadow produced by the straight edge not have a sharp edge?

The light waves are made of wavelets that spread out in all directions and interfere with each other.

Two light waves of equal wavelength, lambda, are emitted in phase from separate sources and propagate to a common point P. Light wave 1 must travel a longer distance (d1) than light wave 2 (d2) to reach point P, where d1 - d2 is equal to the path difference between the two light waves. If the two waves interfere destructively at point P, what must be true about the path difference between the two light waves?

The path difference must be equal to a half-integral number of wavelengths.

Two light waves of equal wavelength, lambda, are emitted in phase from separate sources and propagate to a common point P. Light wave 1 must travel a longer distance (d1) than light wave 2 (d2) to reach point P, where d1 - d2 is equal to the path difference between the two light waves. If the two waves interfere constructively at point P, what must be true about the path difference between the two light waves?

The path difference must be equal to an integral multiple of the wavelength.

Light propagating in a material with index of refraction n1 is incident on a new material with index of refraction n2 < n1. An example of this could be light initially traveling through water and reflecting at a water-air boundary. Some of the incident light reflects at this boundary between materials 1 and 2 and continues to propagate in material 1. How does the phase of the reflected light compare to the phase of the incident light?

The reflected light is in phase with the incident light

Light propagating in a material with index of refraction n1 is incident on a new material with index of refraction n2 > n1. An example of this could be light initially traveling through air and reflecting at an air-water boundary. Some of the incident light reflects at this boundary between materials 1 and 2 and continues to propagate in material 1. How does the phase of the reflected light compare to the phase of the incident light?

The reflected light is one-half cycle out of phase with the incident light.

What does it mean for two light waves to be in phase?

The two waves reach their maximum value at the same time and their minimum value at the same time.

What does it mean for two light waves to be one-half cycle out of phase?

When one wave reaches its maximum value the other wave reaches its minimum value.

Light of wavelength lambda strikes a plane of glass and some of that light reflects while the rest of the light transmits through the glass. The transmitted beam is then reflected from a glass-water interface, as shown in the figure. The light waves reflected from the air-glass interface and the glass-water interface will be one-half cycle out of phase if the thickness of the glass is _______ .

lambda / 2 ( 1.50)

Monochromatic light of wavelength lambda, such as light from a laser, is directed through two narrow parallel slits that are a distance d apart. There is a viewing screen a very long distance R away from the slits that is used to observe the interference pattern that emerges from the light shining through the slits. The distance that light travels from one slit to the screen is r1 and the distance that light travels from the other slit to the screen is r2. The central bright fringe of the interference pattern results due to a path difference, r1 - r2, of zero. What path difference is required to produce the first order dark fringe that is adjacent to the central bright fringe?

r1 - r2 = ± 1/2λ

Monochromatic light of wavelength lambda, such as light from a laser, is directed through two narrow parallel slits that are a distance d apart. There is a viewing screen a very long distance R away from the slits that is used to observe the interference pattern that emerges from the light shining through the slits. The distance that light travels from one slit to the screen is r1 and the distance that light travels from the other slit to the screen is r2. The central bright fringe of the interference pattern results due to a path difference, r1 - r2, of zero. What path difference is required to produce the first order bright fringe that is adjacent to the central bright fringe?

r1-r2 = ±λ

Light of wavelength lambda strikes a plane of glass and some of that light reflects while the rest of the light transmits through the glass. The transmitted beam is then reflected from a glass-water interface, as shown in the figure. The light waves reflected from the air-glass interface and the glass-water interface will be in phase if the thickness of the glass is _______ .

λ / 4(1.50)