Question

Light of wavelength$620\mathrm{nm}$illuminates a diffraction grating. The second-order maximum is at angle $39.5°$. How many lines per millimeter does this grating have?

Short answer

There are$n=512$lines per millimeter does this grating have

Step-by-step solution

Step1:  definition of light of wavelength

As a result, the wavelength is defined as the distance between the crest or trough of one wave and the crest or trough of the next wave. The wavelength of light is defined as "the distance between the light wave's two successive crests or troughs."

Find how many lines per meter

In order to obtain constructive interference from a diffraction grating, the following conditions must be met.

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

$m=0,1,2,3,\dots$

We can use the previous equation to calculate the distance between any two successive slits d if we know the angle of the second-order maximum and the wavelength used to illuminate the grating.

$d=\frac{2\lambda }{\sin {\theta }_2}=\frac{2\times 620\times {10}^{-9}\mathrm{m}}{\sin \left({39.5}^{\circ }\right)}=1.95\times {10}^{-6}\mathrm{m}$

The number of lines per millimetre can now be calculated as

$n=\frac{1\mathrm{mm}}{d}=\frac{1\times {10}^{-3}\mathrm{m}}{1.95\times {10}^{-6}\mathrm{m}}=512$