Question

A concave mirror has a focal length of $20cm$. The distance between the two positions of the object for which the image size is double of the object size is

• A. $20cm$
• B. $40cm$
• C. $30cm$
• D. $60cm$

Answer 1

The correct option is A $20cm$

The focal length of the mirror is $20cm$.

In the case of real image,

The object distance is $u_1$, then the image distance will be $-2u_1$.

The mirror formula is given as,

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\frac{1}{-2u_1}-\frac{1}{u_1}=\frac{-1}{20}$

$u_1=30cm$

In the case of virtual image,

The object distance is $-u_2$, then the image distance will be $2u_2$.

The mirror formula is given as,

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\frac{1}{2u_1}+\frac{1}{-u_1}=\frac{-1}{20}$

$u_2=10cm$

The distance between two positions of object is given as,

$u=30-10$

$=20cm$

Thus the distance between the two positions of object is $20cm$.