Question

A virtual image twice as big as the object is formed by a convex lens when the object is 10 cm away from it. A real image twice as big as the object will be formed when it is placed at a distance from the lens

• A. $40cm$
• B. $30cm$
• C. $20cm$
• D. $15cm$

Answer 1

The correct option is B $30cm$

For a lens the magnification is given as:
$m=\frac{v}{u}\text{For a virtual image}m=\frac{v}{u}=+2,whenu=-10cmv=2u\text{From lens formula}\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\frac{1}{2u}-\frac{1}{u}=\frac{1}{f}f=20cm\text{For real image v is positive and u is negative}\text{hence}v=-2u\frac{1}{(-2u)}-\frac{1}{u}=\frac{1}{f}\frac{1}{f}=-\frac{3}{2u}f=-\frac{2u}{3}u=-30cm$