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Question

When the plane surface of a plano-convex lens of refractive index 1.5 is silvered, it behaves like a concave mirror with f=30 cm.When its convex surface is silvered, it will behave like a concave mirror of focal length:

A
10 cm
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B
20 cm
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C
30 cm
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D
45 cm
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Solution

The correct option is C 30 cm
Let power of lens = PL
Power of mirror=PM

In case of silvering plane surface,
Refraction will take place through curve part twice,
And reflection will take place through plane part once.

P=2PLPM=2PL=2fL=130cm1( as power of plane mirror=0)

By lens maker formula,

1fL=(μ1)1R

160=12R

R=30cm

PM=10030m1

In case of silvering convex surface,

Refraction will take place via the plane part twice and
Reflection will take place through curve part once.

PL=0 here as plane part won't refract like a lens.

P=2PLPM=PM=10030m1

P=1f=130cm1

Focal length of the equivalent concave mirror = 30 cms.

Option C is correct answer.

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