JEE Main · 2022 · 29 Jun 2022 · Shift 1 · Wave Optics

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Using Young's double slit experiment, a monochromatic light of wavelength 5000 Å produces fringes of fringe width 0.5 mm . If another monochromatic light of wavelength

6000 \overset{˚}{A}

is used and the separation between the slits is doubled, then the new fringe width will be :

(A)0.5 mm
(B)1.0 mm
(C)0.6 mm
(D)0.3 mm✓ Correct

Answer: (D)

Solution

Fringe width is given by

β = \frac{D λ}{d}

.

Initially:

β_{1} = \frac{D \times 5000 \times 1 0 ^{- 10}}{d} = 0.5

mm

After changes:

β_{2} = \frac{D \times 6000 \times 1 0 ^{- 10}}{2 d}

Taking the ratio:

\frac{β _{2}}{β _{1}} = \frac{6000 \times 1 0 ^{- 10} / ( 2 d )}{5000 \times 1 0 ^{- 10} / d} = \frac{6000}{2 \times 5000} = \frac{3}{5}

β_{2} = \frac{3}{5} \times 0.5 = 0.3

JEE Main · 2022 · 29 Jun 2022 · Shift 1 · Single correct option

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