In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by $5 \times 10^{-2} \mathrm{~m}$ towards the slits, the change in fringe width is $3 \times 10^{-3} \mathrm{~cm}$. If the distance between the slits is 1 mm, then the wavelength of the light will be ______ nm.

JEE Main · 2022 · 29 Jun 2022 · Shift 2 · Wave Optics

In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by

5 \times 1 0^{- 2} m

towards the slits, the change in fringe width is

3 \times 1 0^{- 3} cm

. If the distance between the slits is 1 mm, then the wavelength of the light will be ______ nm.

Answer: 600

Solution

The fringe width in a double-slit experiment is:

β = \frac{λ D}{d}

where

λ

is the wavelength,

D

is the screen distance, and

d

is the slit separation.

The change in fringe width when the screen is moved:

Δ β = \frac{λ}{d} Δ D

Rearranging for wavelength:

λ = \frac{Δ β \cdot d}{Δ D}

Substituting values:

$Δ β = 3 \times 1 0^{- 3}$ cm $= 3 \times 1 0^{- 5}$ m
$d = 1$ mm $= 1 \times 1 0^{- 3}$ m
$Δ D = 5 \times 1 0^{- 2}$ m

λ = \frac{3 \times 1 0 ^{- 5} \times 1 \times 1 0 ^{- 3}}{5 \times 1 0 ^{- 2}} = 6 \times 1 0^{- 7} m = 600 nm

JEE Main · 2022 · 29 Jun 2022 · Shift 2 · Integer answer

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JEE Main · 2022 · 29 Jun 2022 · Shift 2 · Wave Optics

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