Question

A 500 lines per mm diffraction grating is illuminated by light of wavelength 640 nm.

1. What is the maximum diffraction order seen? Express your answer as an integer.

2. What is the angle of each diffraction order starting from zero diffraction order to the maximum visible diffraction order? Enter your answers in degrees in ascending order separated by commas.

Answer 1

Solution :

Given :

slit separation (d) = (1/500) mm = 2 x 10^-6 m

wavelength () = 640 nm = 640 x 10^-9 m

Part (A) Solution :

let the maximum order of fringe is m

Then : m = d sin(90)

m (640 x 10^-9 m) = (2 x 10^-6 m)(1)

m = 3.125 = 3

Thus : the maximum diffraction order seen is 3.

Part (B) Solution :

for the first order fringe, m = 1 :

Since :  m = d sin

(1)(640 x 10^-9 m) = (2 x 10^-6 m) sin

₁ = 18.66^o

for the Second order fringe, m = 2 :

Since :  m = d sin

(2)(640 x 10^-9 m) = (2 x 10^-6 m) sin

₂ = 39.79^o

for the Third order fringe, m = 3 :

Since :  m = d sin

(3)(640 x 10^-9 m) = (2 x 10^-6 m) sin

₃ = 73.74^o