Question

A biconvex lens of local length 30 cm has radii of curvature of surfaces in ratio 3 : 2. It is cut into two ti form two plano-convex lenses. Then the focal length of two lenses are

• A. 120 cm, 90 cm
• B. 60 cm, 40 cm
• C. 75 cm, 50 cm
• D. 50 cm, 25 cm

Answer 1

The correct option is C 75 cm, 50 cm

$\frac{1}{30}=(\mu -1)\times (\frac{1}{3R}+\frac{1}{2R})\therefore \frac{(\mu -1)}{R}=\left(\frac{1}{25}\right).......\left(1\right)\therefore \frac{1}{f_1}=(\mu -1)\times \frac{1}{3R}=\frac{1}{3}\times \frac{1}{25}\Rightarrow f_1=75cmAnd\frac{1}{f_1}=(\mu -1)\times \frac{1}{2R}=\frac{1}{2}\times \frac{1}{25}\Rightarrow f_2=50cm$