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Question

The plane surface of a plano- convex lens is silvered. If μ be the refractive index and R, the radius of curvature of curved surface, then the system will behave like a concave mirror of radius of curvature of

A
μR
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B
R(μ1)
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C
R2μ
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D
(μ+1μ1)R
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Solution

The correct option is B R(μ1)
Let fl and fm be the focal lengths of convex lens and the plane mirror (plane polish surface) respectively, then combined power of system,
P=PM2PL

1F=1fm2fl

Since, fp=, So

1F=2fl....(1)

Now, from lens maker's formula for plano-convex lens,

1fl=(μ1)R.....(2)

From (1) and (2),

1F=2(μ1)R

F=R2(μ1)

Here negative sign of effective focal length indicates that combination acts as concave mirror.

Therefore,

the radius of curvature =2|F|

=2(R2(μ1))

=R(μ1)


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