Question

The curvature radii of a concavo-convex glass lens are `20cm`and `60cm`.th convex surface of the lens is silvered .With the lens horizotnal ,the concave surface is filled with water.The focal length of the effective mirror is (`mu`of glass=`1.5,mu`of water=`4//3`
A. `90//13cm`
B. `80//13cm`
C. `20//3cm`
D. `45//8cm`

Answer 1

Correct Answer - A

`R_(1)=60cm,R_(2)=20cm`
`P_(eq)=2P_(1)+2P_(2)+P_(3)`
`(1)/(f_(eq))=(2)/(f_(1))+(2)/(f_(2))-(2)/(f_(3))….(1)`
for lens of water
`(1)/(f_(1))=((4)/(3)-1)((1)/(oo)-(1)/(60))`
`(1)/(f_(1))=(1)/(180)`
For glass lens
`(1)/(f_(2))=((3)/(2)-1) ((1)/(-60)-(1)/(-20))`
`(1)/(f_(2))=(1)/(60)`
for concave mirror `f_(3)=(R )/(2)`
`f_(3)=-10cm`
`(1)/(-f_(eq))=(2)/(180)+(2)/(60)-(1)/(-10)`
`(1)/(-f_(eq))=(26)/(180) rArr f_(eq)=(-90)/(13)cm`