Question

Suppose that you have a transmission diffraction grating with n = 105 lines per mm. Light from a sodium lamp is incident perpendicular to the grating surface (i.e. ?_i = 0), passes through the grating and is diffracted onto a distant screen.

(i) Two (weak) visible lines in the sodium spectrum have wavelengths 498 nm and 569 nm. What is the angular separation ?? of the first order (m = 1) maxima of these spectral lines generated by this diffraction grating?

(ii) How wide (in mm) does this grating need to be to allow you to resolve the two lines 588.995 and 589.592 nm in the second order (m = 2)? These lines are the well known pair of sodium

Answer 1

hus, when light is normally incident on the grating, the diffracted light will have maxima at angles ?_m given by:

It is straightforward to show that if a plane wave is incident at any arbitrary angle ?_i, the grating equation becomes:

When solved for the diffracted angle maxima, the equation is:

FIRST WE HAVE TO FIND DISTANCE

d=1/105*10^-3

=9.52m

find angle for different wavelengths

take difference that will be angular seperation