Define coherent sources of light.

Coherent source of light are those sources which emit continually a light wave having the same frequency, wavelength and in the same phase, or they have a constant phase difference.Coherent sources can be obtained, if the amplitude of an incoming beam of light is divided, This can be done by the process of partial reflection or refraction. These can also be obtained by division of wave front by putting two narrow slits in front of a monochromatic source.

Derive the expression for the intensity at a point where interference of light occurs. Arrive at the conditions for maximum and zero intensity.

Let the two waves S 1 and S 2 from the two coherent sources interfere at a point P. Let their amplitudes be a and the initial phase difference between them be ϕ . Then the displacements produced by S 1 and S 2 will be given as: y 1 = a cos ω t ....(i) y 2 = a cos ωt + ϕ ....(ii) The intensity produced by each wave, I 0 ∝ a 2 ....(iii) The resultant displacement at point P will be: y = y 1 + y 2 y = a cos ω t + cos ω t + ϕ y = 2 a cos ϕ 2 cos ω t + ϕ 2 ......(iv) From (iii), it is clear that the amplitude of the resultant displacement is 2 a cos ϕ 2 and therefore the intensity at that point will be: I ∝ 4 a 2 cos 2 ϕ 2 On using (iii), we get: I = 4 I 0 cos 2 ϕ 2 .....(v) Where I 0 is the intensity of each of the individual sources. Using (v) , For ϕ = 0 , ± 2 π , ± 4 π . . . . . , the intensity will be maximum and given by: I = 4 I 0 For ϕ = ± π , ± 3 π , ± 5 π . . . . , the intensity will be zero: I = 0

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What is interference of light?

Important Questions on Interference of Light

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 7 - Interference of Light>Exercise>Q 4

The ratio of intensity at the centre of a bright fringe to the intensity at a point distance one-fourth of the distance between two successive bright fringes will be

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 7 - Interference of Light>Exercise>Q 5

Two waves of equal frequencies have their amplitudes in the ratio of $3 : 5$ . They are superimposed on each other. Calculate the ratio of maximum and minimum intensities of the resultant wave.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 7 - Interference of Light>Exercise>Q 6

As you have learnt in the text, the principle of linear superposition of wave displacement is basic to understanding intensity distributions in diffraction and interference patterns. What is the justification of this principle?

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 7 - Interference of Light>Exercise>Q 7

Two point sources $S_{1}$ and $S_{2}$ separated by a distance $10 μ m$ emit light waves of wavelength $4 μ m$ in phase. A circular wire of radius $40 μ m$ is placed around the sources as shown in figure, then ( $O$ is the centre of the circle and $O S_{1} = O S_{2}$ )

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 7 - Interference of Light>Exercise>Q 8

For two waves of same shape the ratio of amplitude is

2 : 1

. Find out maximum and minimum ratios of amplitudes and intensities of vibrations within interference region.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 7 - Interference of Light>Exercise>Q 9

In a double-slit interference experiment, the two coherent beams, have slightly different intensities

I

and

I + δ I

. Show that the resultant intensity at the maxima is nearly

4 I

, while at the minima is nearly

\frac{{(δ I)}^{2}}{4 I}

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 7 - Interference of Light>Exercise>Q 10

In a double-slit arrangement, the slits are separated by a distance equal to

100

times the wavelength of the light passing through the slits.
(a) What is the angular separation in radians between the central maximum and an adjacent maximum?
(b) What is the distance between these maxima on a screen

90.0 cm

from the slits?

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 7 - Interference of Light>Exercise>Q 11

What is meant by Constructive interference?

What is interference of light?

Important Questions on Interference of Light

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