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A plano-convex lens when silvered ono 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 20cm. Then, the refractive index of the lens is |
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Answer» `3.0` `(1)/(F)=(2)/(f_(1))+(2)/(f_(m))` or `(1)/(F)=2(mu-1)((1)/(R))+(1)/(oo)` or `F=(R)/(2mu(-1))` Now, `-60=(R)/(2(mu-1))` or `120(mu-1)=R`(i) Again, `(1)/(F)-(1)/(f_(1))+(1)/(f_(1))+(1)/(f_(m))` or `=(2)/(f_(1))+(1)/(R//2)` or `=2(mu-1)((1)/(R))+(2)/(R)` or `=(2)/(R)(mu-1+1)` or`F=(R)/(2mu)` Now, `-20=(-R)/(2mu)` or `40mu=R` (ii) Dividing (i) by (ii), we get `(120(mu-1))/(40mu)=(R)/(R)=1` or ` 120(mu-1)=40mu` or `120mu-40mu=120` or `80mu=120` or `mu=(120)/(80)=(3)/(2)=1.5`  
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