Question

Given a diffraction grating with 8*10 3 lines/cm and a laser producing 450 nm light:

a. What are the angles for the first and second bright fringe from the central fringe?

b. Would you be able to see the 3 rd fringe? If so what is the angle, if not why?

Answer 1

a)

d = slit width = 0.01/8000 = 1.25 x 10^-6 m

= wavelength= 450 x 10^-9 m

for first bright fringe , n = 1

using the equation

d Sin₁ = n

(1.25 x 10^-6) Sin₁ = (1) (450 x 10^-9)

₁ = 21.2 deg

for second bright fringe , n = 1

using the equation

d Sin₂ = n

(1.25 x 10^-6) Sin₂ = (2) (450 x 10^-9)

₁ = 46.1 deg

b)

for second bright fringe , n = 3

using the equation

d Sin₃ = n

(1.25 x 10^-6) Sin₃ = (3) (450 x 10^-9)

Sin₃ = 1.08

Since value of Sin can not be greater than 1

hence we can't see 3rd fringe