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Q.

A plano-convex lens, when silvered at its plane surface is equivalent to a concave mirror of focal length 28cm. When its curved surface is silvered and the plane surface not silvered, it is equivalent to a concave mirror of focal length  10cm, then the refractive index of the material of the lens is:

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a

914

b

149

c

179

d

None

answer is B.

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Detailed Solution

When plane surface is silvered, we use Peq=2PL=2μ−1R Then in case when curved surface is silvered, we use Peq=2PL+Pm , ⇒Peq=2μ−1R+2R=2μR Given that,  feq=28 cmSo we use  28=R2μ−1....1When curved surface is silvered,  we use feq=R2μ=10....2 From equation (1) and (2) we get, μ=149
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