Question

A beam of monochromatic light is diffracted by a slit of width 0.580 mm. The diffraction pattern forms on a wall 1.56 m beyond the slit. The width of the central maximum is 2.05 mm.

Calculate the wavelength of the light.

Answer 1

λ = 381 nm

Step-by-step explanation:

given,

width of slit,a = 0.580 x 10⁻³ m

distance of the screen from the slit, D = 1.56 m

width of central maximum,y = 2.05 x 10⁻³ m

Distance of the edge of central maximum from center of the central maximum y ‘ = y/ 2

Y ‘ = 1.025 x 10⁻³ m

for first maximum

d sin θ = λ

sin θ = tan θ = y'/D

`\lambda = (y'a)/(D)`

`\lambda = (1.025* 10^(-3)* 0.580* 10^(-3))/(1.56)`

λ = 381 x 10⁻⁹ m

λ = 381 nm

wavelength of light is equal to 381 nm.