Answer to Question #164089 in Optics for Bawe

Question

Light is incident normally on a diffraction grating of 5000 lines per centimeter and a second-order image is obtained at an angle of 36°.

            (a.) Calculate the wavelength of the light used, (b.) Determine whether a third-order image can be obtained with light of the same wavelength. (c.) State and explain in which the number of orders can be increased.

                                                                                        

Answer 1

a.)

We have,

$d=5000\\ \theta=36^\circ\\ n=2$

Now, Grating element$= \dfrac{1}{5000} cm = 0.2\times10^{-3}cm = 2\times10^{-6}m$

According to Bragg's law,

$dsin\theta = n\lambda$

$2\times(10^{-6})\times sin36^\circ= 2\lambda$

$\lambda = 0.5877\times10^{-6}\ m$

b.)

Using Bragg's law,

$dsin\theta=n\lambda$

$sin\theta= \dfrac{3\times0.5877\times10^{-6}}{2\times10^{-6}}$

$sin\theta=0.88$

$\theta=61.41^\circ$

Hence, $\theta$ is greater than $2^{nd}$ order image therefore $3^{rd}$ order image cannot be formed.

c.)

Increasing the number of slits not only makes the diffraction maximum sharper, but also much more intense. As the intensity increases, the diffraction maximum becomes narrower as well as more intense.

If we increase the number of lines of grating, correspondingly the grating element  decreases , hence diffraction angle becomes large for given wave length . But, then there is limit on number of lines, because sin(theta) should not become greater than 1.