Question

1. consider now interference of light as it passes through a transmission grating with N slits with a separation h. The light is composed of two wavelengths, λ1 = 500 nm and λ2 = 600 nm. The two wavelengths lead to two interference patterns on a screen.

Some of the interference peaks from the 500 nm light overlap with some interference peaks originating from the 600 nm light. Calculate which interference peaks of the two colors overlap, up to an interference order |m| < 20.

2. (d) (2 points) For 500 slits of separation 1 μm and the screen at a distance of 2 m, calculate the distance between the zero-th order and the 5th order interference peak, for the 500 nm light.

3. (e) (2 points) How wide is the 5th order interference peak of the 600 nm light, for the same transmission grating as in the previous question?

Answer 1

a) Let mth fringe of λ1 overlap with nth fringe with λ2.

Ie., m λ1D/d = n λ2D/d

D-distance of screen from slits

d- distance between the slits

m/n = λ2/λ1= 600 / 500= 6/5

this implies m = 6 and n = 5

Answer: 6th interference peak with light of wavelength λ1 overlap with 5th interference peak with light of wavelength λ2

b) distance between the zero-th order and the 5th order interference peak, for the 500 nm light, x = 5 λ1D/d = 5 x 500 x 10-9 x 2/1 x 10-6 = 5 m

c) the width of 5th order interference peak of 600 nm light, y = λ2D/d = 600 x 10-9 x 2 /1 x 10-6 =1.2m