Question 1

A broad spectrum of light λ = 550 nm) illuminates normally a thin wedge of glass n = 1.50). If the thick edge of the glass is 0.02 mm, the number of dark fringes observed is
A) 109.
B) 99.
C) 73.
D) 55.
E) 33.

Accepted Answer

The answer of  A broad spectrum of light λ...

Question 2

You deposit a thin film of magnesium difluoride on a glass lens n > 1.60), reducing the reflection of yellow light, at normal incidence, to a minimum. You find that the thinnest coating that accomplishes this is 106 nm thick. The index of refraction for MgF2 for yellow light λ = 585 nm) is
A) 1.50.
B) 1.38.
C) 1.15.
D) 1.00.
E) 0.707.

Accepted Answer

The thinnest coating for minimum reflection can be found using the formula:
$t= \frac{\lambda}{4n}$, where t is the thickness of the coating and n is the refractive index of the coating.

Plugging in the given values, we get:
$106	ext{ nm}= \frac{585}{4n}$
Solving for n, we get:
$n=1.38$

Therefore, the answer is B) 1.38.

Question 3

Light of wavelength 640 nm is incident perpendicularly from air onto a film 1000 nm thick and of 1.60 refractive index. When part of the light enters the film and is reflected back at the second face, the number of wavelengths contained along the path of this light in the film is
A) 1.0.
B) 1.6.
C) 2.0.
D) 3.2.
E) 5.0.

Accepted Answer

The answer of Light of wavelength 640 nm is incident...

Question 4

A wedge-shaped film of air is formed by placing a glass plate on a second flat glass plate. The wedge is then illuminated using a monochromatic light from above and a fringe pattern is shown. From the fringe pattern one can conclude that the surface of the first glass plate is
A) much flatter than the wavelength used.
B) flat on the left side but then has a concave to the right side.
C) flat on the left side but then has a convex to the right side.
D) flat on the right side but then has a concave to the left side.
E) flat on the right side but then has a convex to the left side.

Accepted Answer

The answer of  A wedge-shaped film of air is...

Question 5

If we assume normal incidence, the minimum thickness of a soap film n = 1.33) in air that gives constructive interference when viewed by reflected light of wavelength 400 nm is
A) 225 nm.
B) 200 nm.
C) 100 nm.
D) 75 nm.
E) 57 nm.

Accepted Answer

The answer of If we assume normal incidence, the minimum...

Question 6

The interference pattern is from a spherical lens placed on a flat reflecting surface using a monochromatic light of wavelength λ = 550 nm. If the distance from the center to A is 0.6 mm, the radius of curvature of the lens is
A) 41.3 cm.
B) 82.5 cm.
C) 18.7 cm.
D) 37.4 cm.
E) 26.2 cm.

Accepted Answer

The answer of  The interference pattern is from a...

Question 7

Two parallel glass plates of index of refraction n are separated by an air film of thickness d. Light of wavelength λ in air, normally incident on the plates, is intensified on reflection when, for some integer m,
A) 2d = mλ.
B) 2d = mλ/n.
C) 2d = mnλ.
D) 2d = m + 1/2)λ.
E) 2nd = mλ /2.

Accepted Answer

The answer of  Two parallel glass plates of index...

Question 8

You coat a glass lens n = 1.65) with MgF₂ n = 1.38) to reduce reflection. The minimum thickness of coating required to produce destructive interference in reflected light whose wavelength in air is 560 nm is A) 102 nm. B) 140 nm. C) 203 nm. D) 280 nm. E) None of these is correct.

Accepted Answer

The answer of You coat a glass lens n =...

Question 9

You apply a material with n = 1.25 to a lens n_g = 1.5) to make a nonreflective coating due to destructive interference at a wavelength in a vacuum) of 555 nm. What is the minimum thickness of the coating that you need? A) 56 nm B) 110 nm C) 220 nm D) 280 nm E) 140 nm

Accepted Answer

The answer of You apply a material with n =...

Question 10

The interference pattern is from a lens placed on a flat reflecting surface illuminated using a monochromatic light from above. From the pattern one can conclude that the lens
A) is more curved on the left and right sides compared to top and bottom.
B) is more curved on the top and bottom compared to the left and right sides.
C) has a spherical surface.
D) has a concave surface.
E) is none of the above.

Accepted Answer

The interference pattern shows that the surface of the lens is more curved on the top and bottom compared to the left and right sides. This is indicated by the horizontal fringes being more closely spaced than the vertical fringes, which suggests that the surface is shaped like a cylindrical lens. Since the fringes are straight, it can be concluded that the surface is not spherical or concave.

Question 11

Two flat planes of glass are laid on top of one another. The upper plane is slightly raised due to the insertion of a thin piece of paper at one end and an air wedge is thus formed. Light of wavelength 500 nm is normally incident on the glass from above and interference fringes are observed by reflection with 2.5 fringes per cm. Calculate the angle of the wedge. A) 6.3 × 10^-⁵deg B) 1.8 × 10^-³ deg C) 4.0 × 10^-⁴deg D) 3.6 × 10^-³ deg E) 5.7 × 10^-⁴ deg

Accepted Answer

The answer of Two flat planes of glass are laid...

Question 12

At normal incidence, the minimum thickness of a soap film n = 1.33) that causes constructive interference when viewed by reflected light of wavelength 400 nm is
A) 225 nm.
B) 200 nm.
C) 100 nm.
D) 75 nm.
E) 570 nm.

Accepted Answer

The answer of At normal incidence, the minimum thickness of...

Question 13

You place a convex lens on top of a flat plate of glass and illuminate it with monochromatic light of wavelength 600 nm. You observe a dark circle at the center of the lens, surrounded by a series of concentric dark rings. What is the thickness of the air space between the lens and the flat glass plate where you see the sixth dark ring?
A) 3.90 µm
B) 3.60 µm
C) 1.80 µm
D) 1.95 µm
E) 2.10 µm

Accepted Answer

The spacing between the consecutive dark rings in the reflected light is given by:

d = λ/2(n-1/2)

where λ is the wavelength of the incident light and n is the refractive index of the material between the lens and the flat glass plate, which is air in this case.

For the sixth dark ring, n is equal to 1. Therefore, we have:

d = λ/2(6-1/2) = λ/11

Substituting λ = 600 nm, we get:

d = 54.5 nm

The air space between the lens and the flat glass plate where we see the sixth dark ring is equal to the thickness of 11 such dark rings, which gives:

thickness = 11d = 600 nm/11 = 54.5 nm * 11 = 0.6 µm

However, we need the thickness of the air space, which is half of the thickness of the dark ring. Therefore, the answer is:

thickness of air space = 0.6 µm/2 = 0.3 µm = 300 nm = 1.80 µm (approx)

Question 14

You dip a wire loop into soapy water n = 1.33) and hold it up vertically to look at the soap film in white light. The soap film looks dark at the top because it has sagged, and its thickness there is nearly zero, causing the reflected wavelengths to interfere destructively. Partway down the loop you see the first red band of the reflected white light. What is the thickness of the soap film there? Take the wavelength of red light to be 680 nm.)
A) 130 nm
B) 170 nm
C) 220 nm
D) 250 nm
E) 340 nm

Accepted Answer

The answer of You dip a wire loop into soapy...

Question 15

A 3.5-cm-long microscope glass slide has one edge in contact with a flat plane of glass, while the other edge is slightly raised due to the insertion of a thin piece of paper. Sodium light of wavelength 589 nm is normally incident on the glass from above and interference fringes are observed by reflection with a regular spacing of 0.22 mm. Calculate the thickness of the piece of paper. A) 9.4 × 10^-⁵m B) 5.5 × 10^-⁵ m C) 2.4 × 10^-⁵m D) 4.7 × 10^-⁵ m E) None of these is correct.

Accepted Answer

The answer of A 3.5-cm-long microscope glass slide has one...

Question 16

A wedge-shaped film of air is formed by placing two flat glass plates with one end touching each other and the other end spaced by a gold leaf. The wedge is then illuminated using a monochromatic light of wavelength 590 nm from above and the complete fringe pattern is shown. The thickness of the gold leaf is approximately
A) 7.1 µm.
B) 7.4 µm.
C) 6.5 µm.
D) 6.8 µm.
E) 7.8 µm.

Accepted Answer

The answer of  A wedge-shaped film of air is...

Question 17

The interference pattern is from a convex lens placed on a flat reflecting surface using a monochromatic light of wavelength λ = 550 nm. The distance between the lens and the flat surface at position A is
A) 275 nm.
B) 550 nm.
C) 687.5 nm.
D) 825 nm.
E) 962.5 nm.

Accepted Answer

The answer of  The interference pattern is from a...

Question 18

Light of wave length l is incident on two thin films that are in contact and surrounded by air. The top layer is λ/4 thick and has an index of refraction of 1.33. The bottom layer is λ/2 thick and has an index of refraction of 1.50. At normal incidence, the reflected rays that are in phase with each other are
A) 1 and 2.
B) 1 and 3.
C) 2 and 3.
D) 1, 2, and 3.
E) None of these is correct.

Accepted Answer

The answer of  Light of wave length l is...

Question 19

You create a wedge-shaped film of air between two flat plates of glass 2.5 cm wide by laying one on top of the other and placing a small slip of paper 1.0 mm thick between their edges at one end. You illuminate the glass plates with normally incident monochromatic light of unknown wavelength. Observing the reflection, you see dark fringes at both ends of the plates. Between the ends you see three other dark fringes. What is the wavelength of the incident light?
A) 250 nm
B) 400 nm
C) 440 nm
D) 500 nm
E) 620 nm

Accepted Answer

The answer of You create a wedge-shaped film of air...

Question 20

Two optically flat plates lie one on top of the other. A sheet of paper 0.1 mm thick is inserted between the plates at one edge. When the plates are illuminated by light of wavelength 589 nm, the number of interference fringes observed by reflected light is approximately
A) 470.
B) 340.
C) 294.
D) 170.
E) 123.

Accepted Answer

The answer of Two optically flat plates lie one on...

Quiz 23: Wave Properties of Light

A broad spectrum of light λ = 550 nm) illuminates normally a thin wedge of glass n = 1.50) . If the thick edge of the glass is 0.02 mm, the number of dark fringes observed is

You deposit a thin film of magnesium difluoride on a glass lens n > 1.60) , reducing the reflection of yellow light, at normal incidence, to a minimum. You find that the thinnest coating that accomplishes this is 106 nm thick. The index of refraction for MgF2 for yellow light λ = 585 nm) is

Light of wavelength 640 nm is incident perpendicularly from air onto a film 1000 nm thick and of 1.60 refractive index. When part of the light enters the film and is reflected back at the second face, the number of wavelengths contained along the path of this light in the film is

A wedge-shaped film of air is formed by placing a glass plate on a second flat glass plate. The wedge is then illuminated using a monochromatic light from above and a fringe pattern is shown. From the fringe pattern one can conclude that the surface of the first glass plate is

If we assume normal incidence, the minimum thickness of a soap film n = 1.33) in air that gives constructive interference when viewed by reflected light of wavelength 400 nm is

The interference pattern is from a spherical lens placed on a flat reflecting surface using a monochromatic light of wavelength λ = 550 nm. If the distance from the center to A is 0.6 mm, the radius of curvature of the lens is

You coat a glass lens n = 1.65) with MgF₂ n = 1.38) to reduce reflection. The minimum thickness of coating required to produce destructive interference in reflected light whose wavelength in air is 560 nm is

You apply a material with n = 1.25 to a lens n_g = 1.5) to make a nonreflective coating due to destructive interference at a wavelength in a vacuum) of 555 nm. What is the minimum thickness of the coating that you need?

The interference pattern is from a lens placed on a flat reflecting surface illuminated using a monochromatic light from above. From the pattern one can conclude that the lens

At normal incidence, the minimum thickness of a soap film n = 1.33) that causes constructive interference when viewed by reflected light of wavelength 400 nm is

The interference pattern is from a convex lens placed on a flat reflecting surface using a monochromatic light of wavelength λ = 550 nm. The distance between the lens and the flat surface at position A is

Two optically flat plates lie one on top of the other. A sheet of paper 0.1 mm thick is inserted between the plates at one edge. When the plates are illuminated by light of wavelength 589 nm, the number of interference fringes observed by reflected light is approximately