In: Physics
A diffraction grating is made up of slits of width a with separation d. The grating is illuminated by monochromatic plane waves of wavelength λ at normal incidence. What is the angular width of a spectral line observed in the first order if the grating has N slits? State your answer in terms of the given variables. Δθw =
We know from diffraction equations
dsin = m
-------------- (1)
for first order, m = 1
The angular width is given as
w =
/
Ndcos
w =
dsin
/ Ndcos
w =
sin
/ Ncos
from trigonometry, we know that
sin / cos
=
tan
so
w =
tan
/ N
from equation (1)
dsin =
sin =
/
d
= arcsin
(
/ d)
so,
w =
tan (arcsin (
/ d)) / N