A plano-convex lens when silvered on the plane side behaves like a concave mirror of focal length 30cm. However when silvered on the convex side, it behaves like a concave mirror of focal length 10cm. 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 A1.5 Here 1F=2f+1fm Plano-convex lens silvered on plane side has fm=∞ ∴1F=2f+1∞⇒130=2f⇒f=60cm Plano-convex lens silvered on convex side has fm=R2 ∴1F=2f+2R⇒110=260+2R⇒R=30cm Now using 1f=(μ−1)(1R), we get μ=1.5