## APPLICATIONS OF NEWTONS RINGS

Newton’s rings experiment is used to determine the radius of curvature (R) of given lens by knowing the wavelength or vice versa. It is also used to find refractive index of unknown liquid.

### Case 1:-

#### (i) To determine wavelength of a light source:

To find the wavelength ‘λ’ of a given light source, consider a plano-convex lens of radius of curvature ‘R’ and arrange it as shown in the figure.

Due to the air film present between the lens and the glass plate circular rings are formed due to Interference. These rings can be observed using a travelling microscope. The travelling microscope is adjusted so that the centers of the cross-wire are adjusted at the central dark spot. Now rotate the screw then

these rings are moved to the extreme left side and keep the microscope fixed at nth dark ring and reading is noted. Now the microscope is moved to the right side continuously (n-3)th (n-6)th, (n-9) th ……. upto the central dark ring. Again cross the central dark ring and continue rotating the screw in the same direction

upto the extreme right. All the readings are tabulated. The difference between the Dn and Dm of the ring

represents the diameter of the nth and mth dark ring. Substitute the values in the following equation.

𝜆 =𝐷𝑛`2− 𝐷𝑚`2/4(𝑛 − 𝑚)𝑅

Now draw a graph, by taking ring number on the x-axis and diameter of the rings on the y-axis, a straight

line is obtained. Find the slope and substitute it in the following formula which gives wavelength of light

source graphically.

𝐷𝑛`2 − 𝐷𝑚`2/(𝑛 − 𝑚)=𝐴𝐵/𝐶𝐷 = 𝑆𝐿𝑂𝑃𝐸𝜆

=𝑆𝐿𝑂𝑃𝐸/4𝑅

#### (ii) To find refractive index of a liquid:

In order to find the refractive of a unknown liquid, first repeat the experiment using the lens and the glass

plate. The diameters of the mth an nth dark rings are determined using the travelling microscope.

𝐷𝑛`2 − 𝐷𝑚`2 = 4(𝑛 − 𝑚)𝑅. (1)

Now, the plano-convex lens and the plane glass plate is placed in a liquid container whose refractive index

to be determined. Repeat the experiment and diameters of the mth and nth dark rings are measured.

𝐷′𝑛`2 − 𝐷′𝑚`2 =4(𝑛−𝑚)𝑅/𝜇. (2)

From Eq. (1) and (2),

𝜇 =𝐷𝑛`2 − 𝐷𝑚`2/𝐷′𝑛`2 − 𝐷′𝑚`2

### PROBLEMS

1. A parallel beam of light of 6000A0

is incident on a thin glass plate of refractive index 1.5 such that

the angle of refraction into the plate is 500

. find the least thickness of the glass plate which will

appear dark by reflection.

2. In a Newton’s rings experiment, the diameter of the 5th ring is 0.30cm and the diameter of the 15th is

0.62cm. Find the diameter of the 25th ring.

3. A convex lens on a glass plate is exposed to a monochromatic light. The diameter of the 10th dark

ring is 0.433cm. Find the wavelength of the light used if the radius of curvature of the lens is 70 cm.