# 2labman Newtons8

To Determine the Wavelength of Sodium Light using Newton’s Rings

Please read additional instructions on the bench for setting up the PC and camera for this experiment

Introduction

Newton’s rings are interference fringes of equal thickness which are produced in the air film between a convex surface and an optical flat. It is interesting to note that these interference fringes, which demonstrate the wave nature of light, should be credited to Newton who was the chief proponent of the corpuscular theory. The apparatus is set up as shown (Fig. 8.1). L is a convex lens placed on an optically flat plate of glass P, forming an air film of varying thickness. Light from the sodium lamp S, strikes a sheet of glass G, set at an angle such that the light is reflected downwards towards the lens and plate, P. Some of the amplitude is reflected at the lower convex lens surface and some at the glass plate. These two reflected rays travel upwards and enter the microscope and since they are coherent, they interfere in a way which depends on the phase difference introduced by the air film. Since the air film is symmetric about the point of contact, the fringes, which follow lines of equal thickness, will be concentric rings with their centre at this point. They are called fringes of equal thickness. This is an example of interference fringes produced by division of amplitude.

Background

Consider a ray of light incident on the airfilm at a point where its thickness is t. The optical path difference between the two reflected rays will be 2t. Taking into account the phase change of π for reflection at the rare to dense surface, the conditions for constructive and destructive intereference are

2t =

m+

1

λ

2

(constructive interference or bright rings)

8-1

Experiment8. To Determine the Wavelength of Sodium Light using Newton’s Rings

Travelling Microscope

Sodium Lamp

G

L

P

Figure 8.1: Apparatus for observing Newton’s rings

(8.1)

2t = mλ

(destructive interference or dark rings)

where m is the order of the ring and can take the values m = 0, 1, 2, 3 . . ..

R

R-t

t

r

Figure 8.2: Geometry of Newton’s rings arrangement

If R is the radius of curvature of the lens and r, the distance of the point under consideration to the point of contact of the lens and glass plate (see Fig. 8.2) then R2 = (R − t)2 + r2

8-2

Experiment8. To Determine the Wavelength of Sodium Light using Newton’s Rings

Dc : Diameter of

the central

ring

Lm

L3

L2

L1

R2

R1

Right hand side

Left hand side

R3

Rm

Figure 8.3: Measure the diameter of the central ring (Dc ) and the positions of the rings on the left hand (L1 to LM ) and right hand sides (R1 to RM ).

= R2 − 2tR + t2 + r2

r2

D2

2t =

=

R

4R

(8.2)

since t2

r2 and D = 2r diameter of a ring.

Combining this with the condition for, say the mth dark ring, Eq. 8.1, one gets for the diameter of that ring:

2

Dm

= 4Rmλ

(8.3)

hence λ can be determined.

This is the equation used to determine λ. The same equation would be obtained if the bright rings had been taken.

Experimental Procedure

Measure the diameter of the central ring (DC ) and the positions of the rings on the left hand (L1 to LM ) and right hand sides (R1 to RM ) (Fig. 8.3).

The diameter of the mth ring is given by:

Dm = |Lm − L1 | + Dc + |Rm − R1 |

Using Eq. 8.3, calculate the mean λ and the standard error on the mean. 8-3

Experiment8. To Determine the Wavelength of Sodium Light using Newton’s Rings

Table 8.1: Sample data table

Ring Number

Lm

| Lm - L1 |

Rm

| Rm - R1 |

Dm

24

23

22

..

1

Spherometer

A spherometer is used to find R, the radius of curvature of the lens. The lens is a segment of a sphere of radius R. The three legs of the spherometer form a equilateral triangle of side C and lie on a circle of radius a (Fig. 8.3).

The zero of the spherometer is checked using the plane surface of the optical...

References: 1. ‘Physics’, D. Giancoli

2. ‘Optics’, Hecht & Zajac

8-12

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