​ An equiconvex lens of radius R = 1/6m is having power P. Another Bi convex lens of radii R1 and R2 is having same power P, then ​

Question

An equiconvex lens of radius \(R = \frac{1}{6}m\) is having power P. Another Bi convex lens of radii \(R_1\) and \(R_2\) is having same power P, then

(1) \(R_1 = \frac{1}{9}m, R_2 = \frac{1}{3}m\)

(2) \(R_1 = \frac{1}{6}m, R_2 = \frac{1}{3}m\)

(3) \(R_1 = \frac{1}{9}m, R_2 = \frac{1}{4}m\)

(4) \(R_1 = \frac{1}{4}m, R_2 = \frac{1}{5}m\)

Answer 1

Correct option is: (1) \(R_1 = \frac{1}{9}m, R_2 = \frac{1}{3}m\)

\(\frac{1}{f_1} = (\mu - 1) (\frac{2}{R}) = (\mu - 1)12\)

\(\frac{1}{f_2} = (\mu - 1) \left( \frac{1}{R_1} + \frac{1}{R_2} \right) = (\mu - 1) 12\)

\(\frac{1}{R_1} + \frac{1}{R_2} = 12\)