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

`1.67`

Explanation

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_(2)))`
`(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_(1) = - 50 cm`
`(1)/(f_(1)) = ((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)) = 0.1 = 0.9 , mu_(l) = (1.5)/(0.9) = 1.67`