Application of Air Wedge - Thickness of a Thin Sheet of Paper

APPLICATION OF AIR WEDGE ‒ THICKNESS OF A THIN SHEET OF PAPER

Using the principle of airwedge, we can find the thickness of any thin materials, like paper, wire, hair etc.

Principle

Two plane glass plates are inclined at an angle (θ) by introducing a thin material (e.g. hair), forming a wedge shaped air film. This film is illuminated by sodium light. Interference occurs between the two rays, one reflected from the front surface and the other by internal reflection at the back surface. Therefore straight line fringes parallel to the edge of the wedge are obtained. Using the theory of airwedge the thickness of the material can be determined.

Description

Two optically plane glass plates are placed one over the other and tied by means of a rubber band at one end. The given material of wire (or) paper is introduced on the other end, so that an air‒wedge is formed between the plates as shown in Fig. 8.3.

This set up is placed on the horizontal bed plate of the travelling microscope. Light from the source 'S' can be made to fall on the Air wedge setup with the help of a condensing lens(L) and 45° angled glass plate(G).

Working

Light from the sodium vapour lamp (S) is rendered parallel by means of a condensing lens (L). The parallel beam of light is incident on a plane glass plate (G) inclined at an angle of 45⁰ and gets reflected. The reflected light is incident normally on the glass plates in contact P_c.

Interference takes place between the light reflected from the top and bottom surfaces of the glass plates and is viewed through the travelling microscope (M). Since the thickness of the material remains constant in the direction parallel to the thin edge of the wedge, a large number of equally spaced dark and bright straight line fringes are formed parallel to the edge of contact as a shown in Fig. 8.4.

The microscope is adjusted so that the bright (or) dark fringe near the edge of contact is made to coincide with the vertical cross wire and this is taken as the n^th fringe. The reading from the horizontal scale of the travelling microscope is noted.

The microscope is moved across the fringes transverse screw and the readings are taken when the vertical cross wire coincides with every successive 5 fringes (5, 10, 15, 20...). The width of every 20 fringes is calculated and the width of one fringe is calculated. The mean of this gives the fringe width (β).

We know from the theory of Airwedge, the fringe width β = λ/2θ          ....(1)

If ‘l’ is the distance between the edge of contact and the material (say the distance of the last fringe) and 't' is the thickness of the material, then

For θ being very small, from Fig. 8.5, we can write θ = t/l.               ………..(2)

Substituting equation (2) in (1), we get

Fringe width β = λl / 2t

Thickness of the material (t) = λl / 2β

Thus, by finding λ,l and β the thickness of any thin material like, papers, wire, hair, etc., can be determined using air wedge.