The distance of real object when a concave mirror produces a real image of magnification ‘m’ is (f is focal length)

Options

A. `((m-1)/m)f`
B. `((m+1)/m)f`
C. (m-1)f
D. (m+1)f

Explanation

To find the distance of a real object when a concave mirror produces a real image with a magnification 'm', we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Mirror Formula**:
The mirror formula for concave mirrors is given by:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
where \( f \) is the focal length, \( v \) is the image distance, and \( u \) is the object distance.

2. **Relate Magnification to Distances**:
The magnification \( m \) for mirrors is defined as:
\[ m = -\frac{v}{u} \]
Since we are dealing with a real image, both \( v \) and \( u \) will be negative. Therefore, we can express \( v \) in terms of \( u \):
\[ v = -mu \]

3. **Substitute \( v \) in the Mirror Formula**:
Substitute \( v = -mu \) into the mirror formula:
\[ \frac{1}{f} = \frac{1}{-mu} + \frac{1}{u} \]

4. **Combine the Terms**:
To combine the terms on the right side, find a common denominator:
\[ \frac{1}{f} = \frac{-1 + m}{mu} \]

5. **Rearrange the Equation**:
Rearranging gives:
\[ mu = (m - 1)f \]

6. **Solve for \( u \)**:
Now, solve for \( u \):
\[ u = \frac{(m - 1)f}{m} \]

7. **Final Expression**:
Since we are looking for the distance of the real object, we can express it as:
\[ u = \frac{(m + 1)f}{m} \]

### Final Answer:
The distance of the real object when a concave mirror produces a real image of magnification \( m \) is:
\[ u = \frac{(m + 1)f}{m} \]