A beam of light converges to a point on a screen S. A mirror is placed in front of the screen at a distance of 10cm form the screen. It is found that the beam now converges at a point 20cm in front of the mirror. Find the focal length of the mirror.

Explanation

To solve the problem, we will use the mirror formula and the information given in the question. Let's break it down step by step.

### Step 1: Understand the Setup
We have a screen at the origin where light converges at point S. A mirror is placed 10 cm in front of the screen. The light beam, after reflecting off the mirror, converges at a point 20 cm in front of the mirror.

### Step 2: Define the Variables
- Let the distance from the mirror to the screen be \( d = 10 \) cm.
- The distance from the mirror to the point where the light converges after reflection is \( v = -20 \) cm (negative because it is in front of the mirror).
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