A thin gollow equiconvex lens, silvered at the back, converges a parallel beam of light at a distance of 0.2 m in front of it. Where will it converge the same light if filled with water having `mu=(4//3)`?

Explanation

`(1)/(F)=(1)/(f_l)+(1)/(f_m)+(1)/(f_l)=(1)/(f_l)+(1)/(f_m)`
`(1)/(0.2)=0+(1)/(f_m)implies(1)/(f_m)=(1)/(0.2)implies(1)/((R)/(2))=(1)/(0.2)`
`R=0.4cm`
`(1)/(F')=(1)/(f_(l'))+(1)/(f_m)+(1)/(f_(l'))=(2)/(f_(l'))+(1)/(f_(m))`
`=2((4)/(3)-1)((1)/(+0.4)-(1)/(-0.4))+(1)/(0.2)`
`=(2)/(3)((2)/(0.4))+(1)/(0.2)=(1)/(0.3)+(1)/(0.2)=(2+3)/(0.6)`
`F'=(0.6)/(5)m=(60)/(5)cm=12cm`
The rays will converge at focus i.e., 12 cm from lens.