Question

A convex lens forms an image of a distant object at a distance of 20 cm from it. On keeping another lens in contact with the first, if the image is formed at a distance of 40/3 cm from the combination, then the focal length of the second lens is:

• A. -20 cm
• B. -40 cm
• C. 40 cm
• D. 13.33 cm

Answer 1

Answer: (C)

40 cm

Image of a distant object is formed at the focus.

The image due to first lens is formed at 20 cm. Hence, $f_1=20cm$

The image due to combined lens is formed at 40/3 cm. Hence, $f_{eq}=\frac{40}{3}$

$f_{eq}=\frac{f_1{f}_2}{f_1+f_2}\Rightarrow f_{eq}=\frac{20\times f_1}{20+f_1}=\frac{40}{3}$

$3f_1=40+2f_1$

$f_1=40cm$