A thin glass (refractive index 1.5) lens has optical power of `-5D` in air. Its optical power in a liquid medium with refractive index 1.6 will be

Options

A. `-1D`
B. `1D`
C. `-25D`
D. `25D`

Answer

B

Explanation

`(1)/(f_a)=((1.5)/(1)-1)((1)/(R)-(1)/(R))` ….(i)
`(1)/(f_m)=((mu_g)/(mu_m)-1)((1)/(R_1)-(1)/(R_2))`
`(1)/(f_m)=((1.5)/(1.6)-1)((1)/(R_1)-(1)/(R))` ….(ii)
Dividing (i) by (ii), `(f_m)/(f_a)=((1.5-1)/((1.5)/(1.6)-1))=-8`
`P_a=-5=(1)/(f_a)impliesf_a=-(1)/(5)`
`impliesf_m=-8xxf_a=-8xx-(1)/(5)=(8)/(5)`
`P_m=(mu)/(f_m)=(1.6)/(8)xx5=1D`