Question

A double convex lens ( $ {{R}_{1}} $ = $ {{R}_{2}} $ = 100cm) having focal length equal to the focal length of a concave mirror. The radius of the concave mirror is

• A. 10 cm
• B. 20 cm
• C. 40 cm
• D. 15 cm

Answer 1

Answer: (B)

Focal length of convex lens $ \frac{1}{f}=(\mu -1)\left[ \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right] $ $ {{R}_{1}}=10\,cm, $ $ {{R}_{2}}=-10\,cm, $ $ \mu =1.5 $ $ \frac{1}{f}=(1.5-1)\left[ \frac{1}{10}-\frac{1}{-10} \right] $ $ =0.5\left( \frac{2}{10} \right) $ $ f=\frac{10}{2\times 0.5} $ $ f=10\,cm $ Focal length of concave mirror = 10 cm $ \therefore $ Radius of curvature $ =2\times 10=20\,cm $