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_i)-(mu_1) /(-oo) = (mu_2 -mu_1)/(+R ) `…..(i)
for refraction at `2^(nd) ` 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 length of the given lens system is `(mu_3 R )/( mu_3 -mu_1)`