Question

1.    Instead of blocking out all light except what passes through a slit to get an interference pattern, we can block out only the slit and get an equivalent pattern. This is called Babinet’s Principle. You effectively saw Babinet’s Principle when you put the hair in front of the laser. Describe how you could use “single slit diffraction” to measure the size of the hair?

2.    Frequently, photographs of bright lights will result in a “star” effect on the film. This is a diffraction pattern produced by the aperture (opening) inside the lens. How does the magnitude of this effect depend on the size of the aperture?

Answer 1

calculating the diameter of hair with single slit diffraction.

1. As we have an idea about the Babinet’s principle , if we place a hair in front of a laser than a pattern will show on the wall. It is something like as shown in figure

This pattern is formed due to the addition (interference) of light waves at different points. For better understanding consider two waves generated in still water. Then the wavefront will intersect with each other like in the second diagram

So at the point of superposition if the waves are in the same phase than it makes a bigger wave (construction interference) bright region in this case.

If the phase is opposite than it is (destructive interference) dark region.

In same fashion the light and dark region is generated in the diffraction pattern.

For calculation the size of hair

We have to calculate the distance between the consecutive two dark lines (2Yn)

The distance of the wall (where the pattern forms) (D)

And the wavelength of light (λ)

Formula of interference

Here d = diameter of the hair

By placing all values in the formula we can get the diameter of the hair.

SOLUTION 2.

As we know that diffraction is the phenomenon of bending of light so when the light enters into the aperture, light bends. The light bends more if the aperture is smaller resulting in increased star effect.