Question

How does intensity profiles of Large opening and Incoherent Light different from the intensity profiles of Small slits with Incoherent Light?

Please use diagram to explain. Thank you in advance for your help.

Answer 1

First, we need to understand what are the differences which get originate when we are having openings of different cross-sections.

When a light beam falls on an opening which is very large, we can treat the opening to consist of a large number of point sources and consequently the light beams which will be treated to emanate from different point sources will get interfere and hence will produce a pattern. This kind of pattern is called the diffraction pattern.

While in the case of slits, which are of very small cross-section, and they are separated from each other we will get an interference pattern overlapping with a diffraction pattern.

Let's treat them separately,

Case a :) Large opening.

The formula which gives the diffraction pattern is:

.............................(1)

where is the intensity at the center of the screen.

the patten which we will get is given in the figure.

This formula is only valid when the light source is monochromatic, in case when the light source is of non-monochromatic in nature then the central fringe will be white in colour but we will get the fringes of different colour depending upon which colour light is interfering constructively. But after a very far distance from the central fringe we will only get the white colour light.

Case b :)Small opening.

In this case we will get alternate dark and bright fringes only when the light source is of monochromatic in nature. But unlike the case of large opening where most of the intensity is confined in the central fringe, here, the intensity of light is evenly distributed in all of the bright fringes. But when the light is non-monochromatic in nature then we will get the same scenario as in the above case i,e, the central fringe will be bright while the surrounding fringes will be of different colour depending upon the wavelength.

This image describes the interference pattern dut to multiple point slits.

This is the intensity distribution due to diffraction pattern of a sngle large slit.

But these images are generated in case of monochromatic light. In case of non-monochramtic light we will get the central fringe of white colour, while the surrounding fringes will be of different colour.

Hope you get what you were asking, PLease give your valuable feedbac.

Thanks.