In case of a real and inverted image, the magnification of a mirror is

Options

A. positive
B. negative
C. zero
D. infinity

Answer

To solve the question regarding the magnification of a mirror when a real and inverted image is formed, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding the Image Characteristics**:
- We are given that the image formed is real and inverted. This indicates that the image is formed on the same side as the object in the case of a concave mirror.

2. **Magnification Formula**:
- The magnification (M) of a mirror is given by the formula:
\[ M = -\frac{v}{u} \]
where \( v \) is the image distance and \( u \) is the object distance.

3. **Sign Convention**:
- According to the sign convention for mirrors:
- The object distance \( u \) is taken as negative (since the object is placed in front of the mirror).
- The image distance \( v \) for a real image is positive (as it is formed on the same side as the object).

4. **Assigning Values**:
- Let’s assume the object distance \( u = -x \) (where \( x \) is a positive integer).
- Since the image is real, we can assume \( v = y \) (where \( y \) is also a positive integer).

5. **Calculating Magnification**:
- Substitute the values of \( v \) and \( u \) into the magnification formula:
\[ M = -\frac{y}{-x} = \frac{y}{x} \]
- Since \( y \) and \( x \) are both positive integers, \( M \) is positive.

6. **Considering Inversion**:
- The problem states that the image is inverted. For an inverted image, the magnification is negative. Therefore, we conclude:
\[ M = -\frac{y}{x} \]

7. **Final Conclusion**:
- Since the image is real and inverted, the magnification of the mirror is negative.

### Final Answer:
The magnification of a mirror when a real and inverted image is formed is negative.

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