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.

Answer 1

Data: D = 2 m, y_1d = 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

Answer 2

Given:

D = 2 m, a = 0.2 mm = 2 × 10^-4 m, y_1d = 5 mm 

Width of central maxima = 2y_1d = 2 × 5 mm 

= 10 mm = 10 × 10^-3 m 

To find: Wavelength of light (λ)

Formula: Width of central maxima, W_c = `(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.