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

Question

Infinity Learn · Accepted Answer

$$1F=1f1+1f1+1fm1F=2f1+1fmor$$    $$1F=2$$μ−$$11R+1$$∞or   $$F=R2($$μ−$$1)Now$$,      −$$60=$$−$$R2$$μ−$$1or$$  $$120$$μ−$$1=R$$  .  .  .  $$.1Again$$,     $$1F=1f1+1f1+1fmor$$  $$1F=2f1+1R/2or$$  $$1F=2$$μ−$$11R+2Ror$$  $$1F=2F$$μ−$$1+1or$$   $$F=R2$$μNow,   −$$20=$$−$$R2$$μ  or  $$40$$μ$$=R$$   .   .   $$.2Dividing1$$  by  $$2$$,  we  $$get120$$μ−$$140$$μ$$=RR=1or$$   $$120$$μ−$$1=40$$μor   $$120$$μ−$$40$$μ$$=120or$$     $$80$$μ$$=120or$$   μ$$=12080=32=1.5$$

A planoconvex lens when silvered on the plane side behaves like a concave mirror of focal length 60 cm. However. r.l,hen 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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