A long cylindrical tube containing water in closed by an equinvex lens of local length 10 cm in air. A point source is placed along the axis of the tube outside it at a distance of 21 cm from the lens. Locate the final image of the source. Refractive index of the materials of the lens =1.5 and that of water =1.33.

Explanation

First ditermine radius of curvature of lens.
`(1)/(f)=(mu-1)((1)/(R_1)-(1)/(R_2))`
`(1)/(10)=((3)/(2)-1)((1)/(R)-(1)/(-R))impliesR=10cm`
Refraction at (1):
`mu_1=1,mu_2=(3)/(2),u=-21cm,R=10cm,v=?`
`(mu_2)/(v)-(mu_1)/(u)=(mu_2-mu_1)/(R)`
`((3)/(2))/(v)-(1)/(-21)=((3)/(2)-1)/(10)`
`(3)/(2v)+(1)/(21)=(1)/(20)implies(3)/(2v)=(1)/(20)-(1)/(21)=(1)/(420)`
`v=630cm`
Refraction at (2):
`I_1` acts as object
`mu_1=(3)/(2),mu_2=(4)/(3),u=630cm,R=-10cm,v=?`
`((4)/(3))/(v)-((3)/(2))/(630)=((4)/(3)-(3)/(2))/(-10)`
`(4)/(3v)-(1)/(420)=(1)/(60)`
`(4)/(3v)=(1)/(60)+(1)/(420)=(7+1)/(420)=(8)/(420)`
`v=70cm`