Object is placed 15 cm from a concave mirror of focal length 10 cm, then the nature of the image formed will be

Options

A. magnified and inverted
B. magnified and erect
C. small in size and inverted
D. small in size and erect

Explanation

To determine the nature of the image formed by a concave mirror when an object is placed 15 cm from it, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Object distance (u) = -15 cm (the object distance is negative in the mirror convention).
- Focal length (f) = -10 cm (the focal length is negative for a concave mirror).

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

3. **Substitute the Values into the Mirror Formula**:
Rearranging the formula gives:
\[ \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \]
Substituting the values:
\[ \frac{1}{v} = \frac{1}{-10} - \frac{1}{-15} \]

4. **Calculate the Right Side**:
Finding a common denominator (30):
\[ \frac{1}{v} = -\frac{3}{30} + \frac{2}{30} = -\frac{1}{30} \]

5. **Find the Image Distance (v)**:
Taking the reciprocal gives:
\[ v = -30 \text{ cm} \]

6. **Determine the Nature of the Image**:
- The negative sign indicates that the image is formed on the same side as the object (real image).
- Since the object is beyond the focal point (f = -10 cm), the image is also inverted.

7. **Calculate Magnification (m)**:
The magnification (m) is given by:
\[ m = \frac{v}{u} \]
Substituting the values:
\[ m = \frac{-30}{-15} = 2 \]
This indicates that the image is magnified (twice the size of the object).

### Conclusion:
The nature of the image formed is **real, inverted, and magnified**.

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