Question

Consider the following. (a) Find the angle θ locating the first minimum in the Fraunhofer diffraction pattern of a single slit of width 0.186 mm, using light of wavelength 424 nm. (b) Find the angle locating the second minimum.

Answer 1

a) For Fraunhofer diffraction,

Let a = width of the slit

= wavelength of light

For first minima ,

a×sin₁ =

₁ = angle of diffraction for first minima

For small angles

sin_{1 1}

a×₁ =

₁ = / a

₁ = 424 × 10^-9 / 0.186 × 10^-3

₁ = 2279.57 × 10^-6

₁ = 2.28 × 10^-3 rad

b) For second minima

a×sin₂ = 2×

sin₂ = 2× / a

For small angles

sin

₂ = 2× / a

₂ = 2 × 424 × 10^-9 / 0.186 × 10^-3

₂ = 4.56 × 10^-3 rad