Answer to Question #18795 in Optics for Mark

Question

A grating is 2.6 cm wide. A spectral line of wavelength 439 nm is observed at 41 degrees in order 1. (The order # refers to a specific bright spot. The 1st bright spot right or left of the center in the 1st order bright spot. The 2nd, is the 2nd order bright spot.)

The grating is made up of how many lines?

Answer 1

Formula of diffraction gratingis d*sin(theta) = m*lambda.
d is the line spacing. If the grating width is W and number of lines is N, then
d = W/N.
In our problem, W = 2.6 cm, lambda = 439 nm, theta = 41 deg, m = 1.
N = W/d = W*sin(theta)/(m*lambda) = (2.6 cm)*sin(41 deg)/(1*439 nm) = 38900.
Answer: 38900.