What is the sign of focal lenght of convex mirror ?

Options

A. `+ ve `
B. `-ve `
C. can be `+ ve ` can be `-ve`
D. none of these

Answer

To determine the sign of the focal length of a convex mirror, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Mirror Type**: Recognize that a convex mirror is a diverging mirror. This means it causes parallel rays of light to diverge after reflecting off the surface.

2. **Identify the Sign Convention**: Familiarize yourself with the sign convention used in optics. In the Cartesian coordinate system applied to mirrors:
- The direction towards the object (incoming light) is considered negative.
- The direction away from the object (outgoing light) is considered positive.

3. **Draw the Convex Mirror**: Sketch a convex mirror with its principal axis. Mark the center of curvature (C), the vertex (V), and the focus (F).

4. **Locate the Focus**: For a convex mirror, when parallel rays of light strike the mirror, they appear to diverge from a point behind the mirror. This point is known as the focus.

5. **Determine the Position of the Focus**: In the case of a convex mirror, the focus is located on the side of the mirror opposite to the incoming light (behind the mirror). According to the sign convention, since this point is behind the mirror, it is considered negative.

6. **Conclusion**: Therefore, the focal length (F) of a convex mirror is negative.

### Final Answer:
The sign of the focal length of a convex mirror is negative.

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