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# The question is as follow :{if an object is placed at a distance R from the pole of first surface ,then the real image is formed at a distance R from the pole of the second surface.the refractive index μ of the sphere is given by ? }                     you can use the paragraph given below

we have refraction formula for spherical surface,  .................(1)
where n2 is the refrative index of denser medium, n1 is refrative index of rarer medium,
v is the image distance from pole of spherical surface, u is the object distance and R is radius of curvature.

In the question it is given that real image is formed at a distance R from the pole of second surface.
The ambiguity is whether the real image is formed inside sphere, i.e., left side of second surface or
outside sphere i.e. right side of second surface.

If we consider image is formed at left side of second surface, solution for μ is not arrived from eqn.(1),
hence image formation at left side is not possible.

If we consider image is formed at right side of second surface, then medium in sphere is acting like a medium of lens.

Hence we apply lens formula to get focal length f,    ................(2)
since we have equation for lens,  (1/f) = (1/v) - (1/u)   ........................(3)

using eqn.(2) and (3) and using proper sign convention,

we write for image formation by sphere as,  ............(4)
we get μ = 2 from eqn.(4)
Answered by Expert 29th April 2019, 4:05 PM
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Tags: refraction

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