Question

The plane faces of two identical plano-convex lenses each having a focal length of $ 50\, cm $ are placed against each other to form a usual biconvex lens. The distance from this lens combination at which an object must be placed to obtain a real, inverted image which has the same size as the object is:

• A. 50 cm
• B. 25 cm
• C. 100 cm
• D. 40 cm
• E. 125cm

Answer 1

Answer: (A)

The focal length of the combination is $ \frac{1}{F}=\frac{1}{{{f}_{1}}}+\frac{1}{{{f}_{2}}} $
Given, $ {{f}_{1}}=50\,cm,{{f}_{2}}=50\,cm $
$ \therefore $ $ \frac{1}{F}=\frac{1}{50}+\frac{1}{50}=\frac{2}{50} $
$ \Rightarrow $ $ F=\frac{50}{2}=25\,cm $
Object when placed at centre of curvature forms a real, inverted image of same size as object $ =(2\times 25=50\text{ }cm) $ .