Question

A diffraction grating is illuminated first with red light of wavelength 600 nm and then with light of an unknown wavelength. The fifth-order maximum of the unknown wavelength is located exactly at the third-order maximum of the red light. What is the unknown wavelength?

Answer 1

Diffraction grating equation is,

where n is the order number and a positive integer, is the wavelength of the incident light, d the slit width and is the angle of emergence of the diffacted light for which a bright fringe is observed.

Now, for the red light beam, = 600 nm = 600 * 10^-9 m and n = 3

Thus, from the diffraction grating equation,

3 * 600 * 10^-9 = d sin                    Equation (1)

For the beam of unknown wavelength, n = 5. Hence, from the diffraction grating equation,

5 = d sin               Equation (2)

d sin in equation (1) and (2) are same since the red light and the light with unknown wavelength are incident on the same slit and the maximum are observed at exactly the same position in both cases.

Substituting the value of d sin from equation (1) in equation (2), we get,

5 = 3 * 600 * 10^-9

= 3 * 600 * 10^-9 / 5

= 360 * 10^-9 m = 360 nm is the wavelength of the second light.