Question

What should be the value of distance d so that final image is formed on the object itself. (focal lengths of the lenses are written on the lenses).

• A. 10 cm
• B. 5 cm
• C. 20 cm
• D. none of these

Answer 1

Answer: (A)

By lens maker formula $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}=(\frac{{\mu }_L}{{\mu }_M}-1)(\frac{1}{R_1}-\frac{1}{R_2})$

note:- positive direction is direction of incident ray so all the values of u and v are taken accordingly with sign.

For convex lens :

$\frac{1}{f_1}=\frac{1}{v_1}-\frac{1}{u}$

$\frac{1}{10}=\frac{1}{v_1}-\frac{1}{(-10)}$

$v_1=\infty$

For concave lens :

Image of convex lens will now behave object for concave lens

$\frac{1}{f_2}=\frac{1}{v_2}-\frac{1}{v_1}$

$\frac{1}{-20}=\frac{1}{v_2}-\frac{1}{\left(\infty \right)}$

$v_2=-20$ cm

$10+d=20$

$d=10$