Find the focal length of the lens shown in Fig . The radii of curvature of both the surfaces are equal to R.

Answer

A, C

Explanation

For an object placed at infinity the image after first refraction will be formed at a distance `v_1`
`(mu_2)/(v_1)=(mu_1)/(-infty)=(mu_2-mu_1)/(+R)` ….(i)
Image afte second refraction will be formed at distance `v_2`
`(mu_3)/(v_2)-(mu_2)/(v_1)=(mu_3-mu_1)/(+R)` ...(ii)
Adding (i) and (ii) ,
`(mu_3)/(v_2)-(mu_3-mu_1)/(R)impliesv_2=(mu_3R)/(mu_3-mu_1)`
Final image is formed at the focus when incident rays are parallel.
Therefore, focal length will be`(mu_3R)/(mu_3-mu_1)`