Question 1

The minimum path difference that will produce a phase difference of 180º for light of wavelength 600 nm is

Accepted Answer

The phase difference between two waves can be given by:

Δφ = 2πΔx/λ

Where, 
Δφ = Phase difference 
Δx = Path difference 
λ = Wavelength of light

For a phase difference of 180º,

Δφ = π 
2πΔx/λ = π 
Δx = λ/2

Putting the value of λ = 600 nm, we get

Δx = 300 nm

Therefore, the minimum path difference that will produce a phase difference of 180º for light of wavelength 600 nm is 300 nm. The correct option is (C).

Question 2

Which,if any,of the following conditions is not necessary for the light waves from two sources to be coherent?

Accepted Answer

For two light waves to be coherent, they need to have the same frequency (or wavelength, which is directly related to frequency) and a constant phase difference. The same amplitude is not a necessary condition for coherence.

Question 3

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?

Accepted Answer

The dark ring formation is due to interference of light waves reflected from the top and bottom surfaces of the air layer between the lens and the glass plate. The radius of the nth dark ring is given by
r_n = sqrt(nλR), 
where λ is the wavelength of light, R is the radius of the lens, and n is the order of the ring. The thickness of the air layer, t, at the center of the lens is given by
t = (r_n)^2 / (nλ). 
For the sixth dark ring (n=6), 
r_6 = sqrt(6 x 600 x 10^-9 x 0.01 / (4pi)) = 0.282 mm. 
Thus, 
t = (0.282 x 10^-3)^2 / (6 x 600 x 10^-9) = 1.80 µm. 
Therefore, the best choice is (C) 1.80 µm.

Question 4

Two side-by-side coherent light sources radiate at 450 nm.The phase difference between these two sources at a point in space is 0.333 radians.The path difference between the two sources could be

Accepted Answer

The answer of Two side-by-side coherent light sources radiate at...

Question 5

Two side-by-side coherent light sources radiate at 600 nm.The phase difference between these two sources at a point in space is 0.582 radians.The path difference between the two sources could be

Accepted Answer

We know that the path difference between two coherent sources can be calculated using the formula:

path difference = (phase difference in radians) x (wavelength)

Substituting the given values, we get:

path difference = 0.582 x 600 x 10^-9

path difference = 0.3492 x 10^-6 m

path difference = 55.6 nm

Therefore, the path difference between the two sources is 55.6 nm, which is closest to option B.

Question 6

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?

Accepted Answer

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

Question 7

Which of the following statements is true?

Accepted Answer

All of the statements are true. 
A) When two harmonic waves of the same frequency and wavelength but differing in phase combine, the resultant wave is a harmonic wave whose amplitude depends on the phase difference. This is known as interference.
B) A phase difference between two waves can be the result of a difference in path length. This is because one wave may have to travel a longer distance than the other to reach a certain point.
C) A path difference of one wavelength is equivalent to no phase difference at all. This is because one complete wavelength corresponds to a complete cycle, and a phase shift of one cycle ultimately brings the wave back to its initial state.
D) A phase difference between two waves can be the result of reflection from a boundary surface. This is because the phase of the reflected wave may be shifted compared to the incident wave, depending on the nature of the boundary surface.

Question 8

Diffraction of sound waves is more readily observable than that of light waves because

Accepted Answer

Diffraction is the bending of waves around obstacles or through openings. This phenomenon is more readily observable in sound waves than in light waves because sound waves are longitudinal, meaning that the particles vibrate back and forth parallel to the direction of wave travel, while light waves are transverse, meaning that the particles vibrate perpendicular to the direction of wave travel. This allows sound waves to bend around corners or through small openings more easily than light waves.

Question 9

The minimum path difference that will produce a phase difference of 90º for light of wavelength 500 nm is

Accepted Answer

For two coherent sources of light, the path difference required to produce a phase difference of 90º can be calculated using the formula:

Δx = λ/4

where Δx is the path difference and λ is the wavelength of light.

Substituting the given values, we get:

Δx = λ/4 = 500 nm/4 = 125 nm

Therefore, the minimum path difference that will produce a phase difference of 90º for light of wavelength 500 nm is 125 nm.

Hence, the best choice is B.

Question 10

Two waves,one with amplitude A and the second with amplitude 2A,are out of phase by 180S1U1P1$\circ$S1S1P0.The resultant intensity is

Accepted Answer

The equation for the resultant intensity of two waves out of phase by 180 degrees is given by: I = I1 + I2 + 2√(I1*I2)*cos(Δφ) where I1 and I2 are the intensities of the two waves, Δφ is the phase difference between them. Here, I1 = A^2 and I2 = (2A)^2 = 4A^2 Thus, I = A^2 + 4A^2 + 2√(A^2 * 4A^2)*cos(180°) I = 5A^2 - 2A^2 = 3A^2 Therefore, the resultant intensity is 3A^2 or A² (option C).

Question 11

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?

Accepted Answer

The minimum thickness of the coating is one-quarter of the wavelength in the material, or:$$t = \frac{\lambda}{4n} = \frac{555 	ext{ nm}}{4(1.25)} = 110 	ext{ nm}$$

Question 12

For us to see interference phenomena in a thin film,

Accepted Answer

The answer of For us to see interference phenomena in...

Question 13

Two waves,one with amplitude A and the second with amplitude 2A,are in phase.The resultant intensity is

Accepted Answer

The intensity of a wave is proportional to the square of its amplitude. When two waves are in phase, their amplitudes add before squaring. Thus, the resultant amplitude is $A + 2A = 3A$, and the intensity, being proportional to the square of the amplitude, is $(3A)^2$.

Question 14

For two identical rays of light to interfere destructively,their path lengths

Accepted Answer

Destructive interference occurs when the path length difference between two waves is an odd multiple of half wavelength. So, for two identical rays of light to interfere destructively, their path lengths must differ by an odd number of half wavelengths.

Question 15

Two side-by-side coherent light sources radiate at 633 nm.At a point in space where the path difference to these two sources is 30 nm,the phase difference could be

Accepted Answer

The answer of Two side-by-side coherent light sources radiate at...

Question 16

Two side-by-side coherent light sources radiate at 480 nm.At a point in space where the path difference to these two sources is 50 nm,the phase difference could be

Accepted Answer

The answer of Two side-by-side coherent light sources radiate at...

Question 17

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.Part way 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.)

Accepted Answer

The thickness of the soap film for the first red band is calculated using the formula for constructive interference in thin films: $2nt = m\lambda$, where $n$ is the refractive index, $t$ is the thickness, $m$ is the order of interference (for the first band, $m = 1$), and $\lambda$ is the wavelength in the medium. Solving for $t$ gives $t = \frac{m\lambda}{2n} = \frac{1 \times 680 \, \text{nm}}{2 \times 1.33} \approx 170 \, \text{nm}$.

Question 18

Visible light from an ordinary source such as a sodium lamp can be used to produce interference effects that demonstrate the wave nature of light,provided that

Accepted Answer

Interference effects require two or more light waves to interact with each other. In order for this to occur, the light beam must be split into two (or more) beams that have a constant phase relationship, meaning that the crests and troughs of the waves align with each other. This can be achieved by using a beamsplitter or a diffraction grating, for example. Polarization is not necessary for interference effects to occur.

Question 19

A phase shift of 180º occurs when a light wave

Accepted Answer

A phase shift of 180º occurs when a light wave reflects from the boundary surface of a medium that is more dense than the medium in which the wave is traveling.

Question 20

The different colors seen on a soap bubble are produced by

Accepted Answer

The different colors seen on a soap bubble are due to the interference of light that is reflected from the front and back of the soap film. As the light waves reflect off the two surfaces, they interfere constructively and destructively, creating interference patterns that appear as different colors to the human eye.

Quiz 33: Interference and Diffraction

The minimum path difference that will produce a phase difference of 180º for light of wavelength 600 nm is

Which,if any,of the following conditions is not necessary for the light waves from two sources to be coherent?

Two side-by-side coherent light sources radiate at 450 nm.The phase difference between these two sources at a point in space is 0.333 radians.The path difference between the two sources could be

Two side-by-side coherent light sources radiate at 600 nm.The phase difference between these two sources at a point in space is 0.582 radians.The path difference between the two sources could be

Which of the following statements is true?

Diffraction of sound waves is more readily observable than that of light waves because

The minimum path difference that will produce a phase difference of 90º for light of wavelength 500 nm is

Two waves,one with amplitude A and the second with amplitude 2A,are out of phase by 180^$\circ$.The resultant intensity 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?

For us to see interference phenomena in a thin film,

Two waves,one with amplitude A and the second with amplitude 2A,are in phase.The resultant intensity is

For two identical rays of light to interfere destructively,their path lengths

Two side-by-side coherent light sources radiate at 633 nm.At a point in space where the path difference to these two sources is 30 nm,the phase difference could be

Two side-by-side coherent light sources radiate at 480 nm.At a point in space where the path difference to these two sources is 50 nm,the phase difference could be

Visible light from an ordinary source such as a sodium lamp can be used to produce interference effects that demonstrate the wave nature of light,provided that

A phase shift of 180º occurs when a light wave

The different colors seen on a soap bubble are produced by

Quiz 33: Interference and Diffraction

The minimum path difference that will produce a phase difference of 180º for light of wavelength 600 nm is

Which,if any,of the following conditions is not necessary for the light waves from two sources to be coherent?

Two side-by-side coherent light sources radiate at 450 nm.The phase difference between these two sources at a point in space is 0.333 radians.The path difference between the two sources could be

Two side-by-side coherent light sources radiate at 600 nm.The phase difference between these two sources at a point in space is 0.582 radians.The path difference between the two sources could be

Which of the following statements is true?

Diffraction of sound waves is more readily observable than that of light waves because

The minimum path difference that will produce a phase difference of 90º for light of wavelength 500 nm is

Two waves,one with amplitude A and the second with amplitude 2A,are out of phase by 180 ∘\circ∘ .The resultant intensity is

You apply a material with n = 1.25 to a lens (ng = 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?

For us to see interference phenomena in a thin film,

Two waves,one with amplitude A and the second with amplitude 2A,are in phase.The resultant intensity is

For two identical rays of light to interfere destructively,their path lengths

Two side-by-side coherent light sources radiate at 633 nm.At a point in space where the path difference to these two sources is 30 nm,the phase difference could be

Two side-by-side coherent light sources radiate at 480 nm.At a point in space where the path difference to these two sources is 50 nm,the phase difference could be

Visible light from an ordinary source such as a sodium lamp can be used to produce interference effects that demonstrate the wave nature of light,provided that

A phase shift of 180º occurs when a light wave

The different colors seen on a soap bubble are produced by

Two waves,one with amplitude A and the second with amplitude 2A,are out of phase by 180^$\circ$.The resultant intensity 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?