A thin converging lens made of glass of refractive index `1.5` acts as a concave lens of focal length `50 cm`, when immersed in a liquid of refractive index `15//8`. Calculate the focal length of converging lens in air.

Answer

`20 cm`

Explanation

Here, `mu_(g) = 1.5, f_(l) = - 50 cm`
`mu_(l) = 15//8, f_(a) = ?`
`(1)/(f_(a)) = ((mu_(g))/(mu_(a)) - 1)((1)/(R_(1)) - (1)/(R_(2)))` …(i)
`(1)/(f_(l)) = ((mu_(g))/(mu_(l)) -1)((1)/(R_(1)) - (1)/(R_(2)))` …(ii)
`(1)/(-50) = ((1.5)/(15//8) - 1)((1)/(R_(1)) - (1)/(R_(2)))`
or `(1)/(R_(1)) - (1)/(R_(2)) = +(1)/(50) xx (5)/(1) = (1)/(10)`
From (i), `(1)/(f_(a)) = (1.5 - 1)((1)/(10)) = (1)/(20)`
`f_(a) = 20 cm`