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`.