The linear magnification of a concave mirror is.

Options

A. always positive
B. always negative
C. sometimes positive and sometimes negative
D. cannot predict

Answer

To determine the linear magnification of a concave mirror, we can analyze the behavior of images formed by the mirror under different object placements.

### Step-by-Step Solution:

1. **Understanding the Concave Mirror**:
- A concave mirror has a reflecting surface that curves inward. It has a focal point (F) and a center of curvature (C).

2. **Object Placement**:
- The position of the object relative to the focal point is crucial. There are two main cases to consider:
- Case 1: Object is placed beyond the focal length (|u| > |f|).
- Case 2: Object is placed between the focal length and the mirror (|u| < |f|).

3. **Case 1: Object Beyond Focal Length**:
- When the object is beyond the focal length, the image formed is real and inverted.
- In this case, the image distance (v) is negative according to the sign convention used in optics.
- The magnification (m) is given by the formula:
\[ m = \frac{v}{u} \]
- Since v is negative and u is negative (as per the sign convention), the magnification becomes:
\[ m = \frac{-v}{-u} = \frac{v}{u} \text{ (positive)} \]
- Therefore, the magnification is positive.

4. **Case 2: Object Between Focal Length and Mirror**:
- When the object is placed between the focal point and the mirror, the image formed is virtual and upright.
- In this case, the image distance (v) is positive.
- Using the same magnification formula:
\[ m = \frac{v}{u} \]
- Here, v is positive, and u is negative, so the magnification becomes:
\[ m = \frac{v}{-u} \text{ (negative)} \]
- Therefore, the magnification is negative.

5. **Conclusion**:
- Based on the two cases analyzed, we conclude that the linear magnification of a concave mirror can be:
- Sometimes positive (when the object is beyond the focal length).
- Sometimes negative (when the object is between the focal length and the mirror).

### Final Answer:
The linear magnification of a concave mirror is sometimes positive and sometimes negative.

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