When an object is placed at a distance of 25 cm from a mirror, the magnification is `m_(1)`. The object is moved 15cm farther away with respect to the earlier position, and the magnification becomes `m_(2)`. If `m_(1)//m_(2)=4` , then calculate the focal length of the mirror.

Explanation

To solve the problem step by step, let's break it down:

### Step 1: Identify the initial conditions
We know that the object is placed at a distance of 25 cm from the mirror. According to the sign convention, the object distance (u) is negative for mirrors.
- \( u_1 = -25 \, \text{cm} \)

### Step 2: Determine the new object distance
The object is moved 15 cm farther away from its initial position. Therefore, the new object distance is:
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