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.

Explanation

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 Eqs. (i) and (ii), we get `mu_3/v_2-(mu_2-mu_1)/R or v_2=(mu_3R)/(mu_3-mu_1)`

Therefore, focal length of the given lens system is
`f=(mu_3R)/(mu_3-mu_1)`