Question

The focal length of a convex lens is $20cm$, the focal length of the concave mirror is $30cm$. And the separation between lens and mirror is $90cm$. If the object is placed $60cm$ before the lens, find out the position of an image formed by the concave mirror?

• A. 60 cm from point B
• B. 60 cm from point A
• C. 90 cm from point B
• D. 60 cm left of lens

Answer 1

The correct option is A

60 cm from point B

For lens:
Object distance, u = -60 cm
Focal length of the lens, f = 20 cm
Let the distance of thr image formed by convex lens be v.
$\frac{1}{v}$ - $\frac{1}{u}$ = $\frac{1}{f}$

$\frac{1}{v}$ + $\frac{1}{60}$ = + $\frac{1}{20}$

$\frac{1}{v}$ = $\frac{1}{20}$ - $\frac{1}{60}$ = $\frac{1}{30}$ ⇒ v = $30cm$
So, the image is formed 30 cm to the right of convex lens

Focal length of concave mirror = 30 cm
$\therefore$ radius of curvature = 60 cm
Since the image is formed 30 cm to the right of lens i.e, the centre of curvature of the concave mirror, the final image is also formed there.