An equi-convex glass lens with radius of each face as R is placed in air `(._au_g=3//2)`. "If there is water in the object space and air in the image space and given" `._au_w=4//3`, the focal length of the lens is

Options

A. 4 R
B. 2 R
C. `3(R)/(2)`
D. `R`

Answer

C

Explanation

`mu_1=(4)/(3),mu_2=(3)/(2),mu_3=1,R_1=R,R_2=-R`
`(mu_3)/(f)=(mu_2-mu_1)/(R_1)+(mu_3-mu_2)/(R_2)`
`(1)/(f)=((3)/(2)-(4)/(3))/(R)+(1-(3)/(2))/(-R)=(1)/(6R)+(1)/(2R)=(1+3)/(6R)`
`f=(3R)/(2)`