An object is placed 20 cm in front of a mirror is found to have image 15 cm (a) in front of it, (b) behind the mirror. Find the focal length of the mirror and the kind of mirror in each case.

Explanation

To solve the problem step by step, we will analyze both cases separately: (a) where the image is in front of the mirror and (b) where the image is behind the mirror.

### Case (a): Image is in front of the mirror

1. **Identify the Object Distance (U)**:
- The object is placed 20 cm in front of the mirror.
- According to the sign convention, the object distance (U) is negative.
- Therefore, \( U = -20 \, \text{cm} \).
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