Question

A diffraction grating is ruled with $600$ lines per $mm$. 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 ${15}^{\circ }$ with the normal to grating. What is the frequency of the light? (Given $\sin {15}^{\circ }=0.258$)

• A. $1.2\times {10}^{13}Hz$
• B. $4.7\times {10}^{13}Hz$
• C. $1.9\times {10}^{14}Hz$
• D. $7.0\times {10}^{14}Hz$

Answer 1

The correct option is A $1.2\times {10}^{13}Hz$

The angle of diffraction ${\theta }_n$ for $n^{\text{th}}$ order
$d\sin {\theta }_n=n\lambda$
Where $d=$ spacing between adjacent slits in diffraction grating $=\frac{{10}^{-3}}{600}m$

for first - order $n=1$ , ${\theta }_1={15}^{\circ }$

$\lambda =\frac{d\sin {\theta }_1}{1}=\frac{{10}^{-3}}{600}\sin {15}^{\circ }=4.3\times {10}^{-7}\text{m}$

Frequency of light
$f=\frac{C}{\lambda }=\frac{3\times {10}^8}{4.3\times {10}^{-7}}=7.0\times {10}^{14}Hz$