Question 1

Two sources of light are said to be coherent if they emit waves of:

Accepted Answer

The same frequency with a constant phase difference. Only a steady phase relationship keeps the maxima and minima fixed long enough to be observed.

Question 2

Constructive interference of light occurs when the path difference is:

Accepted Answer

An integral multiple of the wavelength. A path difference of n\lambda brings the two waves into step, giving a bright fringe.

Question 3

A dark fringe is formed when the path difference between two interfering waves is:

Accepted Answer

An odd multiple of half the wavelength. A path difference of (2n-1)\dfrac{\lambda}{2} puts the waves exactly out of step, so they cancel.

Question 4

Two independent sodium lamps cannot produce an observable interference pattern because they are:

Accepted Answer

Not coherent, since their phase difference varies randomly. Light is emitted in short independent bursts from countless atoms, so the phase relationship between two lamps changes far too quickly.

Question 5

In an interference pattern produced by light, the total energy is:

Accepted Answer

Conserved, being redistributed between bright and dark fringes. The energy absent from the minima reappears in the maxima, so the average intensity across the pattern is unchanged.

Question 6

The resultant intensity of two coherent light waves of intensities I_1 and I_2 with phase difference \phi is:

Accepted Answer

I_1 + I_2 + 2\sqrt{I_1I_2}\cos\phi. The final term is the interference term; averaging it over all \phi gives zero, which is why energy is conserved overall.

Question 7

Coherent light sources for an interference experiment are commonly obtained by:

Accepted Answer

Division of wavefront or division of amplitude from a single source. Splitting one beam guarantees a fixed phase relationship. Young's slits divide the wavefront; thin films divide the amplitude.

Question 8

For a sustained interference pattern, the two sources should ideally have:

Accepted Answer

Equal amplitudes and a constant phase difference. Equal amplitudes make the minima completely dark, producing maximum contrast in the pattern.

Question 9

A Fresnel biprism and Lloyd's mirror are both devices used to:

Accepted Answer

Produce two coherent sources from a single source. Both create two virtual images of one slit, which then act as coherent sources and interfere.

Question 10

In an interference pattern of light the ratio of maximum to minimum intensity is 9 : 1. The ratio of the amplitudes of the interfering waves is:

Accepted Answer

2 : 1. \sqrt{\dfrac{I_{\max}}{I_{\min}}} = \dfrac{A_1 + A_2}{A_1 - A_2} = 3, which gives A_1 : A_2 = 2 : 1.

Question 11

At a point where the path difference between two interfering light waves is \dfrac{\lambda}{2}, the fringe observed is:

Accepted Answer

Dark, since the waves are exactly out of phase. A path difference of \dfrac{\lambda}{2} corresponds to a phase difference of \pi, producing complete destructive interference.

Question 12

The phase difference corresponding to a path difference of \dfrac{\lambda}{3} is:

Accepted Answer

\dfrac{2\pi}{3}	ext{ rad}. \Delta\phi = \dfrac{2\pi}{\lambda} 	imes \dfrac{\lambda}{3} = \dfrac{2\pi}{3}.

Question 13

Two coherent light sources have intensities in the ratio 1 : 4. The ratio of maximum to minimum intensity in the pattern is:

Accepted Answer

9 : 1. Amplitudes are in the ratio 1 : 2, so \dfrac{I_{\max}}{I_{\min}} = \left(\dfrac{2+1}{2-1}\right)^2 = 9.

Question 14

Two coherent light waves each of intensity I_0 meet with a phase difference of \pi. The resultant intensity is:

Accepted Answer

Zero. I = 4I_0\cos^2\dfrac{\phi}{2} = 4I_0\cos^2\dfrac{\pi}{2} = 0.

Question 15

Two coherent light waves each of intensity I_0 meet with a phase difference of \dfrac{\pi}{2}. The resultant intensity is:

Accepted Answer

2I_0. I = 4I_0\cos^2\dfrac{\pi}{4} = 4I_0 	imes 0.5 = 2I_0.

Question 16

At a point the path difference between two interfering waves is 2.5\lambda. The interference there is:

Accepted Answer

Destructive. 2.5\lambda = 5 	imes \dfrac{\lambda}{2}, an odd multiple of half a wavelength, so the waves cancel.

Question 17

Two interfering light waves have amplitudes in the ratio 4 : 3. The ratio of maximum to minimum intensity is:

Accepted Answer

49 : 1. Maximum amplitude = 7 and minimum = 1, so the intensity ratio is 7^2 : 1^2 = 49 : 1.

Question 18

At a point the path difference between two interfering waves is 3\lambda. The fringe there is:

Accepted Answer

Bright, since the path difference is an integral multiple of \lambda. An integral number of wavelengths brings the waves back into step, giving constructive interference.

Question 19

Two coherent waves each of intensity I_0 superpose with a phase difference of \dfrac{2\pi}{3}. The resultant intensity is:

Accepted Answer

I_0. I = 4I_0\cos^2\dfrac{\phi}{2} = 4I_0\cos^2 60^\circ = 4I_0 	imes 0.25 = I_0.

Question 20

A glass slab of refractive index 1.5 introduces an optical path difference of 5\lambda for light of wavelength 600	ext{ nm}. Its thickness is:

Accepted Answer

6\,\mu	ext{m}. (\mu - 1)t = 5\lambda \Rightarrow 0.5t = 5 	imes 600 	imes 10^{-9} \Rightarrow t = 6 	imes 10^{-6}	ext{ m}.

Interference of Light — MH-CET Physics MCQs with Solutions

Questions with solutions