An object is placed at a distance of 30 cm from a concave mirror and its real image is formed at a distance of 30 cm from the mirror. The focal length of the mirror is

Options

A. 15 cm
B. 45 cm
C. 30 cm
D. 20 cm

Explanation

To find the focal length of a concave mirror given the object distance and the image distance, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Object distance (u) = -30 cm (negative because it is in front of the mirror)
- Image distance (v) = -30 cm (negative because it is a real image formed in front of the mirror)

2. **Use the Mirror Formula**:
The mirror formula is given by:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
where \( f \) is the focal length of the mirror.

3. **Substitute the Values**:
Substitute \( u \) and \( v \) into the mirror formula:
\[ \frac{1}{f} = \frac{1}{-30} + \frac{1}{-30} \]

4. **Calculate the Right Side**:
\[ \frac{1}{f} = -\frac{1}{30} - \frac{1}{30} = -\frac{2}{30} = -\frac{1}{15} \]

5. **Find the Focal Length**:
Taking the reciprocal gives:
\[ f = -15 \text{ cm} \]

### Final Answer:
The focal length of the concave mirror is \( -15 \) cm.

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