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Question
In Fraunhoffer diffraction by a narrow slit, a screen is placed at a distance of 2 m from the lens to obtain the diffraction pattern. If the slit width is 0.2 mm and the first minimum is 5 mm on either side of the central maximum, find the wavelength of light.
Solution 1
Data: D = 2 m, y1d = 5 mm = 5 × 10-3 m,
a = 0.2 mm = 0.2 × 10-3 m = 2 × 10-4 m
`"y"_"md" = "m" (lambda"D")/"a"`
∴ `lambda = ("y"_"1d" "a")/"D"` ....(∵ m = 1)
`lambda = (5 xx 10^-3 xx 2 xx 10^-4)/2`
λ = 5 × 10−7 m = 5 × 10−7 × 1010 Å = 5000 Å
Solution 2
Given:
D = 2 m, a = 0.2 mm = 2 × 10-4 m, y1d = 5 mm
Width of central maxima = 2y1d = 2 × 5 mm
= 10 mm = 10 × 10-3 m
To find: Wavelength of light (λ)
Formula: Width of central maxima, Wc = `(2λ"D")/"a"`
Calculation:
From formula,
`10 xx 10^-3 = (2 xx lambda xx 2)/(2 xx 10^-4)`
∴ λ = `(10 xx 10^-3 xx 2 xx 10^-4)/(2 xx 2) = 5 xx 10^-7`m
= 5000 Å
wavelength of the light used is 5000 Å.
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