A diffraction grating is ruled with 600 lines per millimetre. When monochromatic light falls normally on the grating, the first order diffracted beams are observed on the far side of the grating each making an angle of `15^@` with the normal to the grating.
What is the frequency of the light?

Options

A. (a) `1.2xx10^(13)Hz`
B. (b) `4.7xx10^(13)Hz`
C. (c) `1.9xx10^(14)Hz`
D. (d) `7.0xx10^(14)Hz`

Answer

D

Explanation

The angle of diffraction `theta_n` for nth order diffraction pattern of the light is given by
`dsin theta_n=nlambda`
where d=spacing between adjacent slits in diffraction grating `=10^-1/600m`
n=1 for first-order diffracted beam.
`theta_1=15^@`
`implies(dsintheta_1)/(1)=(10^-3)/(600)sin15^@=4.3xx10^-7m`
Thus frequency of light,
`f=c/lambda=(3xx10^8)/(4.3xx10^-7)=7.0xx10^(14)Hz`.