Question

A diffraction grating is made with 750 lines per millimeter is illuminated with violet light of wave length 400nm. How many lines can be observed with this grating? If the intense white light is incident on the same diffracting grating what is the angular separation between the violet edge (400nm) and red edge (700nm)? What is the highest order in which the complete visible spectrum can be seen using this grating (λ =400-700nm)?

Answer 1

The basic equation for the n-th order bright line is:

d*sin(angle) = n*wavelength

where d = e-3/750 = (10/6)e-6 = 1.333e-6 (m
=1333 nm

Therefore the order possible is
n =< 1333/[wavelength/(nm)] since sin(angle) =< 1

Since red is the longest wavelength under consideration,
n =< 1333/700 = 1.9

So the highest order is n = 2.

Using the same equation in the reverse:
sin(angle) = n * wavelength / d
= 1 * wavelength/(nm) / 1333
angle = Arcsin(wavelength/(nm)/1333)

for wavelength = 700 nm, angle = 31.68 deg
for wavelength = 400 nm, angle = 17.46 deg

So the angular separation is 31.68 deg - 17.46 deg = 14.22 deg

To find no of lines to be observed with this gating

Use equation,

dsinθ= nλ

plugging values , sinθ = n*(400nm/1333nm)

This gives sinθ < 1 for n= < 3

Thus we can observe lines upto n=3 or 7 lines.