Question

Assume the visible spectrum ranges from 400 nm to 700 nm. A 5.0 cm wide diffraction grating has 2000 lines.

a) What angle is the first diffraction order for the extreme red light?

b) What angle is the first diffraction order for the extreme violet light?

c) What is the width of the first order of visible light projected on a screen 1 m away?

d) What is the width of the second order?

Answer 1

slit width, a = (0.05m ) / 2000 = 2.5 x 10^-5 m

(A) first order, sin(theta) = wavelength / a

sin(theta) = (700 x 10^-9 m) / (2.5 x 10^-5)

theta = 0.028 rad OR 1.604 deg

(B) for violet light , wavelength = 400 x 10^-9 m

so theta = 0.016 rad. Or 0.917 deg

(C) for small angles, d = D(theta)

d = 1m ( 0.028 - 0.016) rad = 0.012 m = 12 mm

(D) for second order,

sin(theta) = 2 (wavelength) / a

so theta_red = 0.056 rad, theta_violet = 0.032 rad

d = (1m) (0.056-0.032)= 0.024 m = 24 mm