A converging lens of refractive index `1.5` and of focal length `15 cm` in air, has the same radii of curvature for both sides. If it is immersed in a liquid of refractive index `1.7`, find the focal length of the lens in the liquid.

Answer

`- 63.75 cm`

Explanation

Here, `mu_(g) = 1.5, f_(a) = 15 cm, R_(1) = R, R_(2) = -R`
`mu_(l) = 1.7, f_(l) = ?`
As `(1)/(f_(a)) = ((mu_(g))/(mu_(a)) - 1)((1)/(R_(1)) - (1)/(R_(2)))`
`:. (1)/(15) = ((1.5)/(1) - 1)((1)/(R) + (1)/(R)) = (1)/(R ), R = 15 cm`
Again `(1)/(f_(l)) = ((mu_(g))/(mu_(l)) - 1)((1)/(R) + (1)/(R))`
`= ((1.5)/(1.7) -1) xx (2)/(15) = (-0.4)/(1.7 xx 15)`
`:. f_(l) = (-1.7 xx 15)/(0.4) = - 63.75 cm`