A $$plano-convex$$ lens when silvered on the plane side behaves like a concave mirror of focal length $$60$$ cm. However, when silvered on the convex side, it behaves like a concave mirror of focal length $$20$$ cm. Then, the refractive index of the lens is

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Infinity Learn · Accepted Answer

$$1F=1f1+1f1+1fm$$⇒$$1F=2f1+1fm$$⇒⇒$$1F=2($$μ$$-1)(1R)+1$$∞⇒$$F=R2$$μ$$(-1)$$⇒$$-60=-R2($$μ$$-1)$$⇒$$120($$μ$$-1)=R1F=1f1+1f1+1fm$$⇒$$1F=2f1+1R/2$$⇒$$1F2($$μ$$-1)(1R)+2R$$⇒$$1F=2F($$μ$$-1+1)$$⇒$$F=R2$$μ⇒$$-20=-R2g$$μ ⇒$$40$$μ$$=RDividing$$ (1) and (2) , we $$get120($$μ$$-1)40$$μ$$=RR=1$$⇒$$120($$μ$$-1)=40$$μ⇒$$120$$μ$$-40$$μ$$=120$$⇒$$80$$μ$$=120$$

A plano-convex lens when silvered on the plane side behaves like a concave mirror of focal length 60 cm. However, when silvered on the convex side, it behaves like a concave mirror of focal length 20 cm. Then, the refractive index of the lens is

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