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Question

A plano-convex lens when silvered on the plane side behaves like a concave mirror of focal length 30 cm. However when silvered on the convex side, it behaves like a concave mirror of focal length 10 cm. The refractive index of its material is

A
1.5
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B
2.0
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C
2.5
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D
3.0
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Solution

The correct option is A 1.5
Here 1F=2f+1fm
Plano-convex lens silvered on plane side has fm=
1F=2f+1130=2ff=60 cm
Plano-convex lens silvered on convex side has fm=R2
1F=2f+2R110=260+2RR=30 cm
Now using 1f=(μ1)(1R), we get μ=1.5

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