An object is at 20 cm from a concave mirror of focal length 10 cm, the nature of image is

Options

A. Real and inverted
B. Virtual and erect
C. Real and 3 times magnified
D. Real and 2 times magnified

Answer

To determine the nature of the image formed by a concave mirror when an object is placed at a distance of 20 cm from the mirror with a focal length of 10 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Focal length (F) of the concave mirror = -10 cm (the focal length is negative for concave mirrors).
- Object distance (U) = -20 cm (the object distance is negative as per the sign convention).

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

3. **Substitute the Values into the Mirror Formula:**
\[ \frac{1}{-10} = \frac{1}{v} + \frac{1}{-20} \]

4. **Rearranging the Equation:**
\[ \frac{1}{v} = \frac{1}{-10} + \frac{1}{20} \]
To simplify, find a common denominator (which is 20):
\[ \frac{1}{v} = \frac{-2}{20} + \frac{1}{20} = \frac{-2 + 1}{20} = \frac{-1}{20} \]

5. **Calculate the Image Distance (v):**
\[ v = -20 \text{ cm} \]

6. **Determine the Nature of the Image:**
- Since the value of \( v \) is negative, this indicates that the image is formed on the same side as the object, which means it is a **real image**.
- Additionally, real images formed by concave mirrors are inverted.

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