Question

Calculate the angle for the third-order maximum of 580-nm wavelength yellow light falling on a diffraction grating with 500 lines/mm.

Answer 1

Answer:

60.46°

Explanation:

Given that, the wavelength of yellow light which is falling on grating is,

$\lambda=580 nm\\\lambda=580\times 10^{-9}m$

The angle is of the order of 3 means m=3.

And number of lines per mm is,

$N=500\frac{lines}{mm}\\N=(500\times 10^{3})\frac{lines}{m}$

Therefore the condition of maxima,

$m\lambda=dsin\theta$

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

And for third order maxima, m=3

$3\lambda=\frac{1}{N} sin\theta\\sin\theta=3 \lambda N$

Therefore,

$sin\theta=3\times 580\times 10^{-9}m\times 500\times 10^{3}m\\sin\theta=0.87\\\theta=sin^{-1} (0.87)\\\theta=60.46^{\circ}$

Therefore, the angle for third order maxima is 60.46°.