Question

A 500 lines per mm diffraction grating is illuminated by light of wavelength 620 nm .

Part B

What is the angle of each diffraction order?

Enter your answers using two significant figures in ascending order separated by commas.

Answer 1

Given that :

diffraction grating, d = 1 / 500 mm = 2 x 10^-3 mm = 2 x 10^-6 m

wavelength, = 620 nm = 620 x 10^-9 m

Part-B : the angle for each diffraction order which is given as -

using an equation, d Sin = m

= Sin^-1 (m / d)

where, m = fringe order = 1

inserting the values in above eq,

₁ = Sin^-1 [(1) (620 x 10^-9 m) / (2 x 10^-6 m)]

₁ = Sin^-1 (0.31)

₁ = 18 degree                                                                   (Answer in two significant figure)

For m = 2,     

₂ = Sin^-1 [(2) (620 x 10^-9 m) / (2 x 10^-6 m)]

₂ = Sin^-1 (0.62)

₂ = 38.32 degree

₂ = 38 degree           (Answer in two significant figure)