Magnification produced by convex mirror is :

Options

A. always positive and greater than one
B. always negative
C. always positive and less than one
D. zero

Answer

To determine the magnification produced by a convex mirror, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Magnification**:
Magnification (M) is defined as the ratio of the height of the image (h') to the height of the object (h). Mathematically, it is expressed as:
\[ M = \frac{h'}{h} \]

2. **Image Formation by Convex Mirror**:
In a convex mirror, when parallel rays of light strike the mirror, they diverge after reflection. If we extend these diverging rays backward, they appear to originate from a point behind the mirror, which is the focal point.

3. **Characteristics of the Image**:
- The image formed by a convex mirror is always virtual, upright, and diminished (smaller than the object).
- Since the image is smaller than the object, the height of the image (h') is less than the height of the object (h).

4. **Analyzing the Magnification**:
Since the image is smaller than the object, the magnification will be:
\[ M < 1 \]
This means that the value of magnification produced by a convex mirror is always less than 1.

5. **Sign of the Magnification**:
The sign of magnification is determined by the orientation of the image. For a convex mirror, the image is upright, which means:
- Height of the image (h') is positive.
- Height of the object (h) is also positive.
Therefore, the magnification is:
\[ M = \frac{h'}{h} > 0 \]
This indicates that the magnification is positive.

6. **Conclusion**:
Based on the analysis, we conclude that the magnification produced by a convex mirror is:
\[ M \text{ is positive and } M < 1 \]

### Final Answer:
The magnification produced by a convex mirror is positive and less than 1.

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