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(a) Can the interference pattern be produced by two independen

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(a) Can the interference pattern be produced by two independent monochromatic sources of light ? Explain.

(b) The intensity at the central maximum $(O)$ in a Young's double slit experimental set-up shown in the figure is $I_{O}$ . If the distance $OP$ equals one-third of the fringe width of the pattern, show that the intensity at point $P$ , would equal $\frac{I _{O}}{4}$ .
(c) In Young's double slit experiment, the slits are separated by $0.5 mm$ and screen is placed $1.0 m$ away from the slit. It is found that the $5^{th}$ bright fringe is at a distance of $4.13 mm$ from the $2^{nd}$ dark fringe. Find the wavelength of light used.

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Exam:

Class 12th Board 2019

Text solutionVerified

a) No. Sustained interference pattern cannot be obtained
Light waves emitted from a source undergoes abrupt phase changes in times of the order of

1 0^{- 10} s

. So light from two independent sources will not have fixed phase relationship and will be incoherent.
b)

x = \frac{β}{3}, path difference = \frac{λ}{3} phase diff = \frac{2 π}{3} I = I_{0} cos^{2} \frac{ϕ}{2} I = I_{0} cos^{2} (\frac{2 π}{3 \times 2}) = I_{0} cos^{2} (\frac{π}{3}) I = I_{0} (\frac{1}{4}) = \frac{I _{0}}{4}

c) Distance of

5^{th}

bright fringe from

2^{nd}

dark fringe

x = \frac{5 λ D}{d} - \frac{3 λ D}{2 d} = \frac{7}{2} \frac{λ D}{d} λ = \frac{2 x d}{7 D} = \frac{2 \times 4.13 \times 1 0 ^{- 3} \times 0.5 \times 1 0 ^{- 3}}{7 \times 1} λ = 0.59 \times 1 0^{- 6} m = 5900 A n g s t ro m

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(a) Can the interference pattern be produced by two independent monochromatic sources of light ? Explain.

(b) The intensity at the central maximum

(O)

in a Young's double slit experimental set-up shown in the figure is

I_{O}

. If the distance

OP

equals one-third of the fringe width of the pattern, show that the intensity at point

P

, would equal

\frac{I _{O}}{4}

.
(c) In Young's double slit experiment, the slits are separated by

0.5 mm

and screen is placed

1.0 m

away from the slit. It is found that the

5^{th}

bright fringe is at a distance of

4.13 mm

from the

2^{nd}

dark fringe. Find the wavelength of light used.

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Question Text	(a) Can the interference pattern be produced by two independent monochromatic sources of light ? Explain. (b) The intensity at the central maximum $(O)$ in a Young's double slit experimental set-up shown in the figure is $I_{O}$ . If the distance $OP$ equals one-third of the fringe width of the pattern, show that the intensity at point $P$ , would equal $\frac{I _{O}}{4}$ . (c) In Young's double slit experiment, the slits are separated by $0.5 mm$ and screen is placed $1.0 m$ away from the slit. It is found that the $5^{th}$ bright fringe is at a distance of $4.13 mm$ from the $2^{nd}$ dark fringe. Find the wavelength of light used.
Topic	Wave Optics
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	139

Text solutionVerified

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