An equi-convex lens of `(mu=3//2)` and focal length 10 cm is held with its axis vertical and its lower surface immersed in water `(mu=4//3)`, the upper surface being in air. At what distance from the lens, will a vertical beam of parallel light incident of the lens be focused?

Explanation

First determine radius of curvature of equi-convex lens
`(1)/(f)=(mu-1)((1)/(R_1)-(1)/(R_2))`
`(1)/(10)=((3)/(2)-1)((1)/(R)-(1)/(-R))=(1)/(R)impliesR=10cm`
Here incident rays are parallel to principal axis i.e., `u=infty` focal length is being asked
`mu_1=1,mu_2=(3)/(2),mu_3=(4)/(3),R_1=10cm,R_2=-10cm`
`(mu_3)/(f)=(mu_2-mu_1)/(R_1)+(mu_3-mu_2)/(R_2)`
`((4)/(3))/(f)=((3)/(2)-1)/(10)+((4)/(3)-(3)/(2))/(-10)`
`(4)/(3f)=(1)/(20)+(1)/(60)=(1)/(15)`
`f=20cm`