Question

A convex lens of focal length 20 cm and another plano convex lens of focal length 40 cm are placed coaxially (see fig). The plano convex lens is silvered on plane surface. What should be the distance d (in cm) so that final image of the object 'O' is formed on O itself ?

• A. 10 cm
• B. 40 cm
• C. 20 cm
• D. 80 cm

Answer 1

The correct option is C 20 cm

After refraction from first lens:-

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f_1}$

$⟹\frac{1}{v}-\frac{1}{-10}=\frac{1}{20}$

$⟹\frac{1}{v}=\frac{1}{20}-\frac{1}{10}=\frac{-1}{20}$

$⟹$image from left lens form at 20cm to left of it.

For right lens-mirror system:-

$u=(20+d)cm$

Now, for image to form at same point $O$, the rays after refraction from right lens should go parallel, so that it retraces its path and image is formed at the point of object itself.

$⟹u=f_2=40cm$

$⟹20+d=40⟹d=20cm$

Answer-(C)