Determination of the thickness of paper by obtaining fringes in wedge shaped air film.

EXPERIMENT NO. 10

AIM:- Determination of the thickness of paper by obtaining fringes in wedge shaped air film.

APPARATUS :- A sodium vapour lamp, a travelling microscope, two microscope slides, a thin paper, a setup consisting of a plane glass plate fixed in holder making an angle of 45 degrees with horizontal direction.

FORMULAE :-

i) The fringe width, beta = (x₂ - x₁) / (N - n)
ii) The wedge angle, theta = lamda / 2 beta
iii) The thickness of paper, t = l x theta = (l x lamda) / (2 x beta) = [l x lamda x (N - n)] / [2 (x₂ - x₁)]

where, x₁ is the position of n^th dark fringe, x₂ is the position of the N^th dark fringe, l is the length of the air wedge and lamda is the wavelength of the sodium light used.

FIGURES :-

PROCEDURE:-

The apparatus is arranged as shown in figure. Two plane glass plates are taken. They are cleaned thoroughly. They are held in contact at one edge. At the opposite edge, a thin paper is inserted between the glass plates. the air-wedge is formed between the lower surface of upper and upper surface of lower glass plate.

The glass plate system is kept on the platform of a travelling microscope. The light from a sodium vapour lamp is rendered parallel with a condensing lens and is made incident on a plane glass sheet held over the wedge at an angle of 45⁰ with the horizontal. The light falling on the sheet is partially reflected which in turn incident normally on the air wedge. Adjusting the arrangement properly, the microscope field of view is made bright to the maximum extent.

The microscope is moved vertically up and down till parallel fringes are visible which are located on the surface of the air film.

By moving the microscope in a horizontal direction, the vertical cross-wire of the microscope is coincided with one of the (n-th) fring in the pattern. It's position is noted down. The microscope is moved further along the length of the air film counting the number of dark fringes. After counting fringes and coinciding the vertical cross wire of the microscope with now the N-th fringe, position of that N-th fringe is noted. The measurements are repeated three times and are recorded in table.

The length of the air film is measured as the distance between the line of contact of glass plates to the inner edge of the paper. the measurement is done using travelling microscope.

OBSERVATIONS:-

a) TO FIND FRINGE WIDTH, beta :

Sr. No.	Position of nth dark fringe			Position of (n+N)th dark fringe			N	Fringe width, beta = [(x₂ - x₁) / N] (cm)	Mean beta (cm)
Sr. No.	MSR (cm)	VSD	TR (x₁) (cm)	MSR (cm)	VSD	TR (x₂) (cm)	N	Fringe width, beta = [(x₂ - x₁) / N] (cm)	Mean beta (cm)
1 2 3

b) TO FIND LENGTH OF THE AIR FILM, l :-

Sr. No.	Reading at the contact edge of glass plates, MSR(cm) + VSD = TR (cm) (s₁)	Reading at the inner edge of thin paper, MSR(cm) + VSD = TR (cm) (s₂)	Length of air film, l = (s₂ - s₁) (cm)	Mean l (cm)
1 2 3

CALCULATIONS:-

i) theta = (lamda) / (2 beta) = .......... radians.
ii) t = l theta = ......... cms.

RESULT:-

i) The fringe width, beta = cms.
ii) The wedge angle, theta = radians.
iii) The thickness of paper = cms.

PRECAUTIONS:-

While using microscope to measure fringe width etc., it is moved in one direction only from left to right or right to left, so that back lash error is avoided.
To achieve good accuracy in the measurements of beta and l, measurements are repeated thrice.