Question

The light shining on a diffraction grating has a wavelength of 495 nm (in vacuum). The grating produces a second-order bright fringe whose position is defined by an angle of 9.34. How many lines per centimeter does the grating have?

Answer 1

The condition principle maxima for diffraction by grating is,

$d\sin \theta =m\lambda$

Here, d is the spacing between the grating lines, $\theta$ is the angle of diffraction, m is the order of the spectrum, and

$\lambda$ is the wavelength of light used.

Rearrange the equation for d.

     $d =\frac{m\lambda}{\sin \theta}$

         $=\frac{2\left (495\times 10^{-9} \textup{ m} \right )}{\sin\left ( 9.34^{\textup{o}} \right )}$

        $=6.1\times 10^{-6} \textup{ m}$

The number of lines per on the grating is,

$N=\frac{1}{d}$

$=\frac{1}{6.1\times 10^{-6} \textup{ m}}$

$=\frac{1}{\left (6.1\times 10^{-6} \textup{ m} \right )\left ( \frac{1 \textup{ cm}}{0.01 \textup{ m}} \right )}$

$=1639.32 /\textup{ cm}$

Therefore, the number of lines per centimeter on the grating approximately is1640.