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Question
In Young’s double-slit experiment, using monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by 5 x 10-2 m towards the slits, the change in the fringe width is 3 x 10-5 m. If the distance between the two slits is 10-3 m, calculate the wavelength of the light used.
Solution
Here, ΔD = 5 x 10-2 m, Δβ = 3 ×10-5 m, d = 10-3 m, λ = ?
We know that fringe width in Young’s double-slit experiment is given by
`"β" = λ "D"/"d"`
Here, since λ and d are constant, we can write
`"Δβ" = λ/"d" "ΔD"`
∴ λ = `"Δβ"/"ΔD" d`
λ = `( 3 xx 10^-5 xx 10^-3)/(5 xx 10^-2)`
λ = `0.6 xx 10^-6 m xx 10^-7 m = 6000Å `
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