To determine of Radius of curvature of a Plano convex lens by Newton’s rings method.

Aim

To determine of Radius of curvature of a Plano convex lens by Newton's rings method.

Apparatus Required:

A convex lens is focal length about 100 cm, two optically plane glass plates, and traveling micro scope, a condensing lens and sodium Vapor lamp.

Description::

The convex lens is placed on the optically plane plate B as shown in the below fig .On the platform of the traveling microscope. A black paper is placed under the glass plate.

The condensing lens C is placed at a distance equal to the focal length of the lens from the sodium Vapor lamps. The emergent parallel beam of the light is directed towards the glass plate A kept directly above the center of the lens and inclined at 45 Degree to the vertical. The beam of light is reflected on the lens L. As a result of interference between the light reflected from the lower surface of the lens and the top surface of the glass plate B. Newton’s rings with alternate bright and dark rings are formed having a black center. The microscope can focus these rings. (It may happen that the center of the ring system is bright. This is due to the presence of dust particles between the lens and the thick glass plate. In such a case the surface of the lens and the glass plate has to be cleaned.)

Procedure:

The microscope is focused at the center of the ring system. The microscope is moved so that the cross wires pass over 16 or 17 dark rings. Then the microscope is moved back until the vertical cross wire is set at the middle (or end) of the 15 ^th dark ring. The reading of the main scale and the number of Vernier coincidences are noted from which the reading of the microscope can be determined. The microscope is moved so that the vertical cross wire is set at the middle of the 14^th dark ring. The readings of the microscope are noted. Similarly the readings of the microscope with crosswire set Successively at the middle of 13^th, 12^th, 11^th etc…………..5th dark ring. The microscope corresponding to 5^th, 6^th, 7^th …. 15^th dark ring on the other side of the center are noted. From these observations the diameters of the 5^th, 6^th, etc………15 ^thdark rings can be found.

The convex lens L is removed and its radius of curvature R is determined either by a spherometer or by Boy’s method. A graph is drawn with number of the dark ring on the x-axis and the square of the diameter (D ²) on the y-axis. The graph is a straight line passing through origin. From the graph the values of Dm ²and Dn ²corresponding to nThe convex lens L is removed and its radius of curvature R is determined either by a spherometer or by Boy’s method. A graph is drawn with number of the dark ring on the x-axis and the square of the diameter (D ²) on the y-axis. The graph is a straight line passing through origin. From the graph the values of Dm ² and Dn ² corresponding to nth and mth rings are found. and mth rings are found.

The wavelength λ of sodium light is found by the formula

λ = D ² _n - D ² _m/4R(n-m) A degree

Radius of curvature can be obtained by

R = D ² _n - D ² _m/4λ(n-m) A degree

On taking the standard wave length of sodium light, the radius of curvature of the lens can be calculated. The value of the radius of the curvature of the lens is verified using spherometer.

Observations:

The observations of the experiment are as follows

Least count=1 MSD/No div in vernier scale

Calculations

R = - D ² _n - D ² _m/4λ(n-m) or R = slope/4λ

Wavelength of sodium light λ= 5893 A degree.

Precautions:

1. While taking the observations the microscope should be moved only in one direction to avoid error due to back lash.
2. The lens L and the glass plate P should be perfectly clean.
3. The slow motion tangent screw alone should be moved in taking the observations.

Result: -

Radius of curvature of the lens=------------------cm.