Question

Suppose that you have a reflection diffraction grating with n= 105 lines per millimeter. Light from a sodium lamp passes through the grating and is diffracted onto a distant screen.

Two visible lines in the sodium spectrum have wavelengths 498 nmand 569 nm. What is the angular separation ?? of the first maxima of these spectral lines generated by this diffraction grating?

How wide does this grating need to be to allow you to resolve the two lines 589.00 and 589.59 nanometers, which are a well known pair of lines for sodium, in the second order (m=2)?

Answer 1

dsin = m

a) n= 105 lines per mm = 105000 lines per m

( 1/ 105000 ) sin = 1 (498 x 10^-9)

1 = sin^-1( 105 x 498 x 10^-6) = 2.997363 degree apprx

( 1/ 105000 ) sin 2= 1 (569 x 10^-9)

2= 3.425176

delta = 0.427813 degree apprx

b)

Chromatic Resolving power,

R = ? / ??= m ( width)( number of lines on grating)

589/ 0.59 = 2(width)( 105)

width = 4.7538 mm apprx