A `4.5 cm` needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Identify the given values
- Height of the needle (object), \( h = 4.5 \, \text{cm} \)
- Distance of the needle from the mirror (object distance), \( u = -12 \, \text{cm} \) (negative because it is measured against the direction of the incident light)
- Focal length of the convex mirror, \( f = +15 \, \text{cm} \) (positive for convex mirrors)

### Step 2: Use the mirror formula
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