An object is kept at a distance 20 cm from a convex mirror of focal length 20 cm. The image will form at

Options

A. infinity
B. focus
C. the position of object
D. 10 cm behind the mirror

Explanation

To solve the problem of finding the image distance formed by a convex mirror when an object is placed at a distance of 20 cm from it, we can use the mirror formula:

### Step-by-Step Solution:

1. **Identify the given values**:
- Object distance (u) = -20 cm (The object distance is taken as negative in mirror conventions for real objects).
- Focal length (f) = +20 cm (The focal length of a convex mirror is positive).

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,
- \( v \) is the image distance,
- \( u \) is the object distance.

3. **Substitute the known values into the formula**:
\[ \frac{1}{20} = \frac{1}{v} + \frac{1}{-20} \]

4. **Rearrange the equation**:
\[ \frac{1}{v} = \frac{1}{20} + \frac{1}{20} \]
\[ \frac{1}{v} = \frac{1 + 1}{20} = \frac{2}{20} = \frac{1}{10} \]

5. **Solve for v**:
\[ v = 10 \text{ cm} \]

6. **Determine the nature of the image**:
Since the value of \( v \) is positive, this indicates that the image is formed on the same side as the object (behind the mirror), which is typical for a convex mirror.

### Final Answer:
The image will form at a distance of 10 cm behind the convex mirror.