1. In Newton’s ring experiment, the diameter of the 5th ring is 0.30 cm and diameter of 15th the ring is 0.62 cm. Find the diameter of the 25th ring.

Diameter of Newton  Ring = 0.97 cm

Newton Rings is an experiment based on principle of  thin film interference

In Newton Rings Experiment the Diameter of   dark ring is given by equation (1)

From the condition given

Putting the values in equation (1) for fifth diameter we get

So  From equation (1) and (4)

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Diameter of Newton’s 5th ring = 0.30 cm

Diameter of Newton’s 15th ring = 0.62 cm

Diameter of Newton’s 25th ring = ?

From Newton’s rings experiment we infer that

D2n+m − D2n = 4λmR

For the 5th and 15th rings we have

D215 − D25 = 4λ * 10 * R (1) (m = 10)

For 15th and 25th rings

D225 − D215 = 4λ * 10 * R (2) (m = 10)

We equate the two derivatives

Equation (2) = Equation (1)

D225 − D215 = D215 − D25

D225 = 2D215 – D25

Substituting the values into the equation

D225 = 2 * 0.62 * 0.62 – 0.3 * 0.3 =0.6788 cm2

D25 = 0.8239 cm

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