Question 1

Light is incident perpendicularly from air onto a liquid film that is on a glass plate. The liquid film is $199 \mathrm {~nm}$ thick, and the liquid has index of refraction 1.60. The glass has index of refraction 1.50. Calculate the longest visible wavelength (as measured in air)of the light for which there will be totally destructive interference between the rays reflected from the top and bottom surfaces of the film. Assume that the visible spectrum lies between 400 nm and 700 nm.

Accepted Answer

The answer of Light is incident perpendicularly from air onto...

Question 2

A 360-nm thick oil film floats on the surface of a pool of water. The indices of refraction of the oil and the water are 1.50 and 1.33, respectively. When the surface of the oil is illuminated from above at normal incidence with white light, what is the wavelength of light between 400 nm to 800 nm wavelength that is most weakly reflected?
A)520 nm
B)540 nm
C)560 nm
D)580 nm
E)600 nm

Accepted Answer

To determine the wavelength of light that is most weakly reflected, we need to find the wavelength at which the reflected light waves from the top and bottom surfaces of the oil film interfere destructively, resulting in minimum reflection. This can be found using the equation:

2nt = mλ

where n is the refractive index of the oil, t is the thickness of the oil film, m is an integer (0,1,2,3...), and λ is the wavelength of light in vacuum.

For minimum reflection, we need to find the first minimum (m=1), which corresponds to the wavelength of light that is most weakly reflected. Plugging in the given values, we get:

2(1.50)(360 nm) = (1)(λ)
λ = 720 nm

This is the wavelength for which the total path difference of the reflected light waves is λ/2, resulting in destructive interference. However, this is outside the given range of 400 nm to 800 nm, so we need to find the closest option. Going down from 720 nm by increments of 20 nm, we get:

700 nm, 680 nm, 660 nm, 640 nm, 620 nm, 600 nm, 580 nm, 560 nm

Therefore, the closest option is 560 nm, which is answer choice B.

Question 3

A sodium light, having wavelength 589.3 nm, is used to view a soap film to make it look black when directed perpendicular to the film. What is the minimum thickness of the soap film if the index of refraction of soap solution is 1.38?
A)114 nm
B)194 nm
C)294 nm
D)314 nm
E)214 nm

Accepted Answer

The answer of A sodium light, having wavelength 589.3 nm,...

Question 4

A 360-nm thick oil film floats on the surface of a pool of water water. The indices of refraction of the oil and the water are 1.5 and 1.33, respectively. When the surface of the oil is illuminated from above at normal incidence with white light, what are the two wavelengths of light between 400 nm to 800 nm wavelength that are most strongly reflected?
A)410 nm and 700 nm
B)430 nm and 720 nm
C)450 nm and 740 nm
D)470 nm and 760 nm
E)490 nm and 780 nm

Accepted Answer

The condition for constructive interference is given by:
2nt = mλ, where n is the refractive index, t is the thickness of the oil film, m is an integer and λ is the wavelength in the medium outside the oil film (in this case, air).

For maximum reflection, we need a high contrast in the refractive indices of the two media, which occurs at normal incidence. Therefore, we consider the wavelengths within the visible spectrum (400 nm to 800 nm).

Using the given values:
n1 = 1.5 (refractive index of oil)
n2 = 1.33 (refractive index of water)
t = 360 nm

For the first maximum (m=1), we have:
2n1t = λ1n2
λ1 = 2n1t/n2 = 430 nm

For the second maximum (m=2), we have:
2n1t = λ2n2
λ2 = 2n1t/2n2 = 720 nm

Therefore, the two wavelengths that are most strongly reflected are 430 nm and 720 nm, which corresponds to option B.

Question 5

A metallic sheet has a large number of parallel slits, 5.0 mm wide and 20 cm apart. This sheet is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is incident normally on the sheet.
- If the microwave wavelength is 6.0 cm, what is the largest angle from the normal, at which an intensity maximum occurs?
A)64°
B)69°
C)74°
D)79°
E)84°

Accepted Answer

The answer of A metallic sheet has a large number...

Question 6

Light has wavelength 600 nm in a vacuum. It passes into glass, which has an index of refraction of 1.5. What is the frequency of the light inside the glass? (c = 3.0 × 10⁸ m/s) A)3.3 × 10¹⁴ Hz B)5.0 × 10¹⁴ Hz C)3.3 × 10⁵ Hz D)5.0 × 10⁵ Hz

Accepted Answer

The frequency of light does not change when it passes from one medium to another. The frequency $f$ can be calculated using the formula $f = \frac{c}{\lambda}$, where $c$ is the speed of light in vacuum and $\lambda$ is the wavelength in vacuum. Given $c = 3.0 \times 10^{8} \, \text{m/s}$ and $\lambda = 600 \, \text{nm} = 600 \times 10^{-9} \, \text{m}$, $f = \frac{3.0 \times 10^{8}}{600 \times 10^{-9}} = 5.0 \times 10^{14} \, \text{Hz}$.

Question 7

A light beam with wavelength 500 nm is reflected constructively from a thin layer of oil having index of refraction 1.25. The oil floats on the top of water of index of refraction 1.33. What is the minimum thickness of the layer of oil?
A)100 nm
B)150 nm
C)175 nm
D)200 nm
E)225 nm

Accepted Answer

For constructive interference to occur, the path difference between the two reflected rays must be an integer multiple of the wavelength. In this case, we have:

2nt = mλ

where n is the refractive index of the oil, t is the thickness of the oil layer, m is an integer, and λ is the wavelength of the light. We want to find the minimum value of t that satisfies this condition.

Using Snell's law, we can find the angle of incidence at the air/oil interface:

sin θ1 = n2 sin θ2
sin θ1 = (1.33/1.25) sin 90° = 1.064
θ1 = 44.1°

Since the oil layer is thin, we can assume that the angle of reflection at the oil/water interface is approximately equal to the angle of incidence at the air/oil interface. Thus, we have:

2t = (m + 1/2)λ/ sin θ1

For the minimum value of t, we take m = 0. Thus,

2t = λ/2 sin θ1

t = λ/4 sin θ1

Plugging in the values, we get:

t = (500 nm)/(4 sin 44.1°) ≈ 201 nm

Therefore, the minimum thickness of the layer of oil is 200 nm, which corresponds to choice D.

Question 8

A glass plate that is 2.5 cm long is separated from another glass plate at one end by a strand of someone's hair that is 0.010 mm in diameter. How far apart are the adjacent interference bands when viewed with light of wavelength 600 nm?

Accepted Answer

The answer of A glass plate that is 2.5 cm...

Question 9

Light has a wavelength of 600 nm in a vacuum. It passes into glass, which has an index of refraction of 1.50. What is the wavelength of the light in the glass?
A)600 nm
B)500 nm
C)400 nm
D)300 nm
E)900 nm

Accepted Answer

The relationship between the wavelength of light in vacuum and the wavelength of light in a medium is given by:

n = λ_vacuum / λ_medium

where n is the refractive index of the medium, λ_vacuum is the wavelength of light in vacuum and λ_medium is the wavelength of light in the medium.

Rearranging the equation to solve for λ_medium, we get:

λ_medium = λ_vacuum / n

Substituting the values given, we get:

λ_medium = 600 nm / 1.5 = 400 nm

Therefore, the wavelength of the light in the glass is 400 nm.

Question 10

A metallic sheet has a large number of parallel slits, 5.0 mm wide and 20 cm apart. This sheet is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is incident normally on the sheet. 
-If the intensity maxima occur 2.0° apart in the central region, what is the wavelength of the microwaves?
A)5.0 mm
B)6.0 mm
C)7.0 mm
D)8.0 mm
E)9.0 mm

Accepted Answer

The distance between the slits, d = 20 cm = 0.2 m, and the width of each slit, a = 5.0 mm = 5.0 x 10^-3 m. The angle between the intensity maxima, θ = 2.0° = 2.0 x π/180 radians. The distance between the central maximum and the first-order maximum is given by:
sinθ = λ/d
λ = d sinθ
λ = 0.2 x sin(2.0° x π/180)
λ = 7.02 x 10^-3 m
λ = 7.0 mm (to two significant figures)

Therefore, the wavelength of the microwaves is 7.0 mm and the best choice is C.

Question 11

A soap bubble has an index of refraction of 1.33. What minimum thickness of this bubble will ensure maximum reflectance of normally-incident light having a wavelength of 530 nm?
A)24.9 nm
B)76.9 nm
C)99.6 nm
D)199 nm
E)398 nm

Accepted Answer

The condition for maximum reflectance from a soap bubble is given by 2nt = mλ, where n is the refractive index, t is the thickness of the bubble, λ is the wavelength of incident light, and m is an integer representing the order of the reflection (m = 1 for the first order).

Plugging in the given values, we get 2(1.33)t = (1)(530 nm), which simplifies to t = 99.6 nm. Therefore, the minimum thickness of the bubble required for maximum reflectance is 99.6 nm.

Thus, the answer is C: 99.6 nm.

Question 12

A metallic sheet has a large number of parallel slits, 5.0 mm wide and 20 cm apart. This sheet is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is incident normally on the sheet. -What is the smallest microwave frequency for which only the central maximum will occur? (c = 3.00 × 10⁸ m/s) A)0.50 GHz B)0.70 GHz C)1.0 GHz D)1.5 GHz E)2.0 GHz

Accepted Answer

The answer of A metallic sheet has a large number...

Question 13

An oil film with refractive index 1.48 and thickness 290 nm is floating on water and illuminated with white light at normal incidence. What is the wavelength of the dominant color in the reflected light?
A)green (541 nm)
B)blue-green (493 nm)
C)violet (404 nm)
D)yellow (572 nm)
E)blue (470 nm)

Accepted Answer

The answer of An oil film with refractive index 1.48...

Question 14

The wavelength of light in a thin film is 360 nm and the wavelength of light in vacuum is 469 nm. What is the index of refraction for the film?
A)1.10
B)1.30
C)1.50
D)1.70
E)1.90

Accepted Answer

The index of refraction of a material can be calculated using the formula:

n = λvacuum/λfilm

where n is the index of refraction, λvacuum is the wavelength of light in vacuum, and λfilm is the wavelength of light in the thin film.

Substituting the given values, we get:

n = 469 nm / 360 nm ≈ 1.30

Therefore, the index of refraction for the film is approximately 1.30. The closest choice to this value is B, which is the correct answer.

Question 15

A soap bubble, when illuminated at normal incidence with light of 463 nm, appears to be especially reflective. If the index of refraction of the film is 1.35, what is the minimum thickness the soap film can be if it is surrounded by air?

Accepted Answer

The answer of A soap bubble, when illuminated at normal...

Question 16

A 500-nm-wavelength beam of light illuminates a soap film with air on both sides and an index of refraction 1.33. If the beam of light is incident normally on the film, what is the minimum thickness of the film to make the reflected light enhanced in brightness?
A)47.0 nm
B)74.0 nm
C)94.0 nm
D)152 nm
E)268 nm

Accepted Answer

For constructive interference (enhanced brightness), the reflected waves must be in phase. This occurs when the path length difference between the two reflected waves is equal to an integer number of wavelengths, or:
2t = mλ/2, where t is the thickness of the film, λ is the wavelength of the incident light in air, m is an integer (1, 2, 3, ...).
Since the light is passing through the soap film twice, we need to use the wavelength of the light in the soap film, which is λ/n = 500 nm / 1.33 = 375 nm. 
So, we have:
2t = m(375 nm)/2 = 187.5 m
t = 187.5 m / 2 = 93.75 nm
Since we need to round up to the nearest whole number (since the thickness cannot be less than the minimum value we just calculated) we get:
t = 94.0 nm, so the answer is (C).

Question 17

Light in air of wavelength 500 nm illuminates a soap film that has an index of refraction of 1.3 and air on both sides. What is the minimum thickness of this film that will produce cancellation in the reflected light when the light is incident normally on the film?

Accepted Answer

The answer of Light in air of wavelength 500 nm...

Question 18

A diffraction grating has 450 lines per millimeter. What is the highest order m that contains the entire visible spectrum from 400 nm to 700 nm?
A)m = 2
B)m = 3
C)m = 4
D)m = 5
E)m = 6

Accepted Answer

The answer of A diffraction grating has 450 lines per...

Question 19

A soap bubble with air on both sides has an index of refraction of 1.33. What minimum thickness of the wall of this bubble will ensure maximum reflectance of normally incident light having a wavelength of 530 nm?

Accepted Answer

The answer of A soap bubble with air on both...

Question 20

What is the minimum thickness of a soap bubble film with refractive index 1.38 that results in a constructive interference in the reflected light if this film is illuminated by a beam of light of wavelength 610 nm?
A)222 nm
B)111 nm
C)333 nm
D)444 nm
E)555 nm

Accepted Answer

The condition for constructive interference in reflected light is given by 2t = mλ/ n, where t is the thickness of the film, λ is the wavelength of incident light, n is the refractive index of the film and m is an integer.
Substituting the given values, we get,
2t = mλ/ n
2t = (1 × 610 nm)/1.38
t = 111 nm
Therefore, the minimum thickness of the soap bubble film required for constructive interference is 111 nm. Thus, the correct answer is option B.

Quiz 17: Wave Optics

A sodium light, having wavelength 589.3 nm, is used to view a soap film to make it look black when directed perpendicular to the film. What is the minimum thickness of the soap film if the index of refraction of soap solution is 1.38?

Light has wavelength 600 nm in a vacuum. It passes into glass, which has an index of refraction of 1.5. What is the frequency of the light inside the glass? (c = 3.0 × 108 m/s)

A light beam with wavelength 500 nm is reflected constructively from a thin layer of oil having index of refraction 1.25. The oil floats on the top of water of index of refraction 1.33. What is the minimum thickness of the layer of oil?

A glass plate that is 2.5 cm long is separated from another glass plate at one end by a strand of someone's hair that is 0.010 mm in diameter. How far apart are the adjacent interference bands when viewed with light of wavelength 600 nm?

Light has a wavelength of 600 nm in a vacuum. It passes into glass, which has an index of refraction of 1.50. What is the wavelength of the light in the glass?

A soap bubble has an index of refraction of 1.33. What minimum thickness of this bubble will ensure maximum reflectance of normally-incident light having a wavelength of 530 nm?

An oil film with refractive index 1.48 and thickness 290 nm is floating on water and illuminated with white light at normal incidence. What is the wavelength of the dominant color in the reflected light?

The wavelength of light in a thin film is 360 nm and the wavelength of light in vacuum is 469 nm. What is the index of refraction for the film?

A soap bubble, when illuminated at normal incidence with light of 463 nm, appears to be especially reflective. If the index of refraction of the film is 1.35, what is the minimum thickness the soap film can be if it is surrounded by air?

A 500-nm-wavelength beam of light illuminates a soap film with air on both sides and an index of refraction 1.33. If the beam of light is incident normally on the film, what is the minimum thickness of the film to make the reflected light enhanced in brightness?

Light in air of wavelength 500 nm illuminates a soap film that has an index of refraction of 1.3 and air on both sides. What is the minimum thickness of this film that will produce cancellation in the reflected light when the light is incident normally on the film?

A diffraction grating has 450 lines per millimeter. What is the highest order m that contains the entire visible spectrum from 400 nm to 700 nm?

A soap bubble with air on both sides has an index of refraction of 1.33. What minimum thickness of the wall of this bubble will ensure maximum reflectance of normally incident light having a wavelength of 530 nm?

What is the minimum thickness of a soap bubble film with refractive index 1.38 that results in a constructive interference in the reflected light if this film is illuminated by a beam of light of wavelength 610 nm?

Light has wavelength 600 nm in a vacuum. It passes into glass, which has an index of refraction of 1.5. What is the frequency of the light inside the glass? (c = 3.0 × 10⁸ m/s)