A thin convergent glass lens `(mu_g=1.5)` has a power of `+5.0D.` When this lens is immersed in a liquid of refractive index `mu_1,` it acts as a divergent lens of focal length `100 cm.` The value of `mu_1` is

Options

A. `(4)/(3)`
B. `(3)/(2)`
C. `(5)/(3)`
D. `2`

Answer

C

Explanation

`(1)/(f_a)=((3)/(2)-1)((1)/(R_1)-(1)/(R_2))` … (i)
`(1)/(f_l)=((3//2)/(._amu_l)-1)((1)/(R_1)-(1)/(R_2))`
(i)/(ii)
`(f_l)/(f_a)=((3//2-1))/(((3//2)/(._amu_l)-1))`
`f_(1)=(100)/(P)=(100)/(5)=20cm`
`f_(l)=-100cm`
`(-100)/(20)=(1//2)/((3/(2_(a)mu_(l))-1))`
`(3)/(2_(a)mu_(l))-1=-(1)/(10)implies(3)/(2_(a)mu_(l))=(9)/(10)`
`._amu_l=(15)/(9)=(5)/(3)`