Question

A concave mirror of focal length $10cm$ and convex mirror of focal length $15cm$ are placed facing each other $40cm$ apart. A point object is placed between the mirrors on their common axis and $15cm$ from the concave mirror. One of the images is produced by the reflection first at concave mirror and then at convex mirror. The distance of this image from convex mirror is

• A. $6cm$
• B. $5cm$
• C. $4cm$
• D. $3cm$

Answer 1

The correct option is A $6cm$



Using mirror formula for first reflection by the concave mirror,
$v=\frac{uf}{u-f}=\frac{(-15)(-10)}{-15+10}$
$=\frac{150}{-5}=-30cm$
This image will behave as the object for the convex mirror

For the reflection at the convex mirror,
$u=-10cm$ and $f=15cm$
(considering the direction in which rays are travelling to be positive)
$v=\frac{uf}{u-f}=\frac{(-10)\left(15\right)}{-10-15}=6cm$