An object is placed in front of the concave mirror of focal length f. The magnification of the image became twice when the object distance is changed from 20 cm to 11 cm. Calculate the value of f.

Explanation

To solve the problem step by step, we will use the mirror formula and the magnification formula for concave mirrors.

### Step 1: Understand the given information
- The object distance changes from \( u_1 = -20 \, \text{cm} \) to \( u_2 = -11 \, \text{cm} \) (negative because the object is in front of the mirror).
- The magnification \( m_2 \) when the object distance is \( u_2 \) becomes twice the magnification \( m_1 \) when the object distance is \( u_1 \): \( m_2 = 2m_1 \).

### Step 2: Write the magnification formulas
The magnification \( m \) for a mirror is given by:
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