Question

A converging lens of focal length 15 cm and a converging mirror of focal length 10 cm are placed 50 cm apart with common principal axis. A point source is placed in between the lens and the mirror at a distance of 40 cm from the lens. Find the locations of the two images formed.

Answer 1

Given:
Convex lens of focal length (f_l) = 15 cm
Concave mirror of focal length (f₂) = 10 cm
Distance between the lens and the mirror = 50 cm
Point source is placed at a distance of 40 cm from the lens.
It means the point source is at the focus of the mirror.
Thus, two images will be formed:
(a) One due to direct transmission of light through the lens.
(b) One due to reflection and then transmission of the rays through the lens.

Case 1:
(S') For the image by direct transmission, we have:
Object distance (u) = − 40 cm
f_l = 15 cm
Using the lens formula, we get:
$$\begin{gathered} \frac{1}{v}-\frac{1}{u}=\frac{1}{f} \\ \Rightarrow \frac{1}{v}=\frac{1}{15}+\frac{1}{(-40)} \\ =\frac{40-15}{40\times 15} \\ \Rightarrow v=\frac{40\times 15}{40-15} \end{gathered}$$

Therefore, v is 24 cm to the left from the lens.

Case II:
(S') Since the object is placed at the focus of the mirror, the rays become parallel to the lens after reflection.
∴ Object distance (u) = ∞ ⇒ f_l = 15 cm
$\Rightarrow \frac{1}{v}-\frac{1}{u}=\frac{1}{15}$
Thus, v is 15 cm to the left of the lens.