Question

A laser emits two wavelengths (λ1 = 420 nm; λ2 = 630 nm). When these two wavelengths strike a grating with 450 lines/mm, they produce maxima (in different orders) that coincide. What is the order (m) of each of the two overlapping lines? At what angle does this overlap occur?

Answer 1

a) angle

m = sin^-1 (m x λ x N)

= sin^-1 [ m (420nm)(450 x 10^-6 nm^-1)]

= sin^-1 [m(0.189)]

now calculate for different m:
for m=1, sigma1= 11 degrees
for m=2, sigma2= 22
for m=3, sigma3= 35
for m=4, sigma4= 49

do the same thing for the wavelength 630 nm
sigma m = sin^-1 [m (0.28350]
then calculate for different m:
for m=1, sigma1= 16
for m=2, sigma2= 35
for m=3, sigma3= 58

now check for which m the angle is the same
here m1= 3 and m2= 2 for angle= 35