Question

An optical system consists of a thin convex lens of focal length 30 cm and a plane mirror 15 cm behind the lens. An object is placed 15 cm in front of the lens. The distance of the final image formed from the lens is

• A. 60 cm
• B. 30 cm
• C. 35 cm
• D. 40 cm

Answer 1

The correct option is A 60 cm

$-30cm\to F=30cm$

$F=+30cm$ $u=-15cm$

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

$\frac{1}{30}=\frac{1}{v}-\frac{1}{-15}$

$\frac{1}{v}=\frac{1}{30}-\frac{1}{15}=\frac{1-2}{30}=\frac{-1}{30}$

$+ve$ image is at $45cm$ from plane mirror so it makes it image as in at $45cm$ in opposite direction

So the distance of final image from convex lens is $(15+45)$

$=60cm$