Question

The focal length of a lens and mirror are $10cm$ and $20cm$ respectively. Find the position of the final image.

• A. $10cm$ behind the concave mirror
• B. $20cm$ in front of concave mirror
• C. $20cm$ behind the concave mirror
• D. $10cm$ in front of concave mirror

Answer 1

The correct option is C $20cm$ behind the concave mirror

Given:
The distance of object from the convex lens, $u=-20cm$
Height of image, $h=5cm$
Focal length of convex lens, $f_1=10cm$.
Focal length of concave mirror, $f_2=-20cm$
(Assuming new cartesian sign convention)
Distance between the mirror and the lens, $d=30cm$

By lens formula,
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$\frac{1}{10}=\frac{1}{v}-\frac{1}{-20}cm$
$v=20cm$
The positive sign show that the image is formed to the right side of the lens.

The image $v$ in front of concave mirror, between pole and focus acts as an object for the concave mirror.
Hence, the object distance from concave mirror, $u^{\prime }=-10cm$

By mirror formula,
$\frac{1}{f_2}=\frac{1}{v^{\prime }}+\frac{1}{u^{\prime }}$
$\frac{1}{-20}=\frac{1}{v^{\prime }}+\frac{1}{-10}$
$v^{\prime }=20cm$
The image formed by concave mirror is $20cm$ behind the mirror.