Question

Babinet’s principle states (roughly) that the diffraction pattern produced by a solid object is the same as the diffraction pattern that would be produced by a hole of the same shape as the object.Can you think of a way in which you could measure the width of a strand of hair using this principle and possibly using interference and diffraction

Answer 1

As per know, we always discussed sending light through very narrow slits or reflecting it off of small grooves, in each case creating a series of point-like “new sources” of light that can then go on and interfere. Rather amazingly, light hitting a small solid object, like a piece of hair, creates the same interference pattern as if the object were replaced with a hole of the same dimensions. This idea is Babinet’s Principle, and the reason behind it is summed up by the pictoral equation at right. If you add an object to a hole of the same size, you get a filled hole. EM waves hitting those objects must add in the same fashion, that is, the electric fields produced when light hits the hole, when added to the electric fields produced by the small object, must add to the electric fields produced when light hits the filled hole. Since no light can get through the filled hole,

Ehole + Eobject = 0.

Thus we find that the electric fields coming out of the hole are equal and opposite to the electric fields diffracting off of the small object. Since the observed interference pattern depends on intensity, the square of the electric field, the hole and the object will generate identical diffraction patterns. By measuring properties of the diffraction pattern we can thus measure the width of the small object. In this lab the small object will be a piece of your hair.

You will shine the light through slits, across hairs and make measurements of the resulting interference pattern.

For this, we can use Young's Double slit:

where, d : distance between slits

   : angle

n : fringe observed

r1 : distance between slit one and n

r2 : distance between slit two and n

yn : distance from center axis and fringe observed(n)

L : distance between slits and screen

According to Babinet's principle, the diffraction pattern of an opaque object will be identical to the diffraction pattern of a hole of the same shape and size, with the exception of the intensity of the light.

This means that a piece of wire or hair will be identical to two slits with the same distance 'd' as the hair. Using this, the width of a piece of hair can be calculated by finding the value of d.