A converging lens and a diverging mirror are placed at a separation of 20 cm. The focal length of the lens is 30 cm and that of the mirror is 50 cm. Where should a point source be placed between the lens and the miror, so that the light, after getting reflected by the mirror and then getting transmitted by the lens, comes out parallel to the principal axis?

Explanation

To solve the problem step by step, we will analyze the situation involving a converging lens and a diverging mirror, and find the position of the point source such that the light exiting the lens is parallel to the principal axis.

### Step 1: Understand the setup
We have a converging lens with a focal length \( f_L = 30 \, \text{cm} \) and a diverging mirror with a focal length \( f_M = -50 \, \text{cm} \). The distance between the lens and the mirror is \( D = 20 \, \text{cm} \).

### Step 2: Set up the coordinate system
Let the position of the point source be \( x \) cm from the lens towards the mirror. Therefore, the object distance for the lens is \( u = -x \) (negative because the object is on the same side as the incoming light).

...