Question

1.For gratings with a larger number of lines per mm, how is the spread of the diffraction pattern affected? Support your argument with theory.

Answer 1

Hey there!

Gratings are components with minute slits within them which makes the light through them split and diffract to different directions. I hope you have a general idea of what a grating us. Now lets look into the concept of what happens when the number of lines increases per sq. mm in the grating.

When it comes to the positions of the maxima and the minima formed by the diffraction pattern , the formula can be given as

where (a + b) is the distance between the 2 slits that is provided, n is the order of spectral lines formed. As n increases we could see that the intensity of the spectral lines formed by the grating decreases . is the wavelength of light. is the angle of diffraction for the n^th order.

First let us consider n=1 , that is the first order maximum. Hence,

Now you could get the idea that if the number of lines increases, the spacing in the grating decreases and hence (a + b) also decreases. Hence the diffraction angle also increases accordingly. But the value of (a + b) can't get above a certain value because the value of cannot go beyond 1. Hence the spectral lines can be obtained by a reasonable increase in the number of lines in the grating and not above the certain value where the value of can be greater than 1.

I hope the solution helps.... Feel free to comment and discuss further... Cheers :)