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In an arrangement for observing Newton's ring of the different media between glass surface, the n th ring have diameter as 10:7 .find the ratio of the refractive indices bof two media?
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In an arrangement for observing Newton's ring of the different media b...
Introduction:
Newton's rings is a phenomenon of interference of light waves when a plano-convex lens is placed on a flat glass plate. The fringes appear as a series of concentric, alternating bright and dark rings.

Given:
Diameter of n-th ring = 10:7
Let the refractive indices of two media be n1 and n2.

Solution:
The diameter of the n-th ring is given by the formula:
Dn = [(n + 1)λR]1/2
where λ is the wavelength of light used and R is the radius of curvature of the plano-convex lens.

Let the diameter of the (n+1)th ring be Dn+1. Then, the ratio of the diameters of the n-th and (n+1)th rings is:
Dn/Dn+1 = [(n+1)/(n+2)]1/2

Given that Dn/Dn+1 = 10/7, we can write:
[(n+1)/(n+2)]1/2 = 10/7
Squaring both sides, we get:
(n+1)/(n+2) = 100/49
49n + 49 = 100n + 100
51n = 51
n = 1

Therefore, the refractive index of one of the media is 1. The refractive index of the other medium can be found using the formula:
n2 = n1(Dn/Dn+1)2

Substituting n1 = 1 and Dn/Dn+1 = 10/7, we get:
n2 = (10/7)2
n2 = 2.04

Conclusion:
The ratio of the refractive indices of the two media is 1:2.04.
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In an arrangement for observing Newton's ring of the different media between glass surface, the n th ring have diameter as 10:7 .find the ratio of the refractive indices bof two media?
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