Question

A single slit of width d = 0.08 mm is illuminated by light of two wavelengths, l = 446 nm and l = 662 nm. The diffraction pattern appears on a screen 1.05 m away. (a) Calculate the angles at which the third dark fringe appears for each wavelength. q446 = rad q662 = rad (b) Calculate the width of the central bright fringe for each wavelength. d446 = m d662 = m

Answer 1

given,

width of slit, d = 0.08 mm

d = 8 x 10⁻⁵ m

light of two wavelength

I₁= 446 nm

I₂ = 662 nm

a) angles at which the third dark fringe

`sin C = (m\lambda)/(d)`

m = 3 , I₁= 446 nm

`sin C = (3* 446 * 10^(-9))/(8* 10^(-5))`

C = 0.958°

m = 3 , I₁= 662 nm

`sin C = (3* 662 * 10^(-9))/(8* 10^(-5))`

C = 1.423°

b) angles at which the third dark fringe

`sin C = (m\lambda)/(d)`

m = 1 , I₁= 446 nm

`sin C = (1* 446 * 10^(-9))/(8* 10^(-5))`

C = 0.319°

m = 1 , I₁= 662 nm

`sin C = (1* 662 * 10^(-9))/(8* 10^(-5))`

C = 0.474°