Question

In the figure, light is incident on a thin lens as shown. The radius of curvature for both the surfaces is R. Determine the focal length of this system.

Answer 1

Correct Answer - `(mu_(3)R)/(mu_(3) - mu_(1))`
For refraction at first surface
`(mu_(2))/(v_(1)) - (mu_(1))/(-oo) = (mu_(2)- mu_(1))/(+R) …. (i)`
For refraction at second surface ,
`(mu_(3))/(v_(2)) - (mu_(2))/(v_(1)) = (mu_(3) - mu_(2))/(+R) ….. (ii)`
Adding equation (i) and (ii) , we get
`(mu_(3))/(v_(2)) = (mu_(3) - mu_(1))/(R) "or" v_(2) = (mu_(3)R)/(mu_(3) - mu_(1))`

Therefore , focal lenght of the given lens system is
`(mu_(3)R)/(mu_(3) - mu_(1))`