Question

A glass convex lens has a power of `+ 10 D` . When this lens is totally immersed in a liquid, it acts as a concave lens of focal length `50 cm`. Calculate the refractive index of the liquid. Given `.^a mu_g = 1.5`.

Answer 1

Correct Answer - `1.67`
Here, `P = + 10 D, .^a mu_g = 1.5` ,
`f_a = (100)/(P) = (100)/(10) = 10 cm`
`(1)/(f_a) = (.^a mu_g - 1) ((1)/(R_1) - (1)/(R_1))`
`(1)/(10) = (1.5 - 1) ((1)/(R_1) - (1)/(R_2))` or `(1)/(R_1)-(1)/(R_2) = (1)/(5)`
When this lens is immersed in liquid, `f_l = -50 cm`
`(1)/(f_l) = ((mu_g)/(mu_l) - 1) ((1)/(R_1) - (1)/(R_2))`
`(1)/(-50) = ((1.5)/(mu_l) - 1) xx (1)/(5)` or `(1.5)/(mu_l) - 1 = -0.1`
or `(1.5)/(mu_l) = 1 - 0.1 = 0.9 , mu_l = (1.5)/(0.9) = 1.67`.