An object is placed at 20 cm from a convex mirror of focal length 20 cm. The distance of the image from the pole of the mirror is

Options

A. `20 cm`
B. infinite
C. `10 cm`
D. depends on the position of the object

Explanation

To find the distance of the image from the pole of a convex mirror, we can use the mirror formula:

\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]

Where:
- \( f \) is the focal length of the mirror,
- \( v \) is the image distance from the mirror,
- \( u \) is the object distance from the mirror.

### 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 is positive for a convex mirror).

2. **Substitute the Values into the Mirror Formula**:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
Plugging in the values:
\[ \frac{1}{20} = \frac{1}{v} + \frac{1}{-20} \]

3. **Simplify the Equation**:
Rearranging the equation gives:
\[ \frac{1}{v} = \frac{1}{20} + \frac{1}{20} \]
\[ \frac{1}{v} = \frac{1 + (-1)}{20} = \frac{2}{20} \]
\[ \frac{1}{v} = \frac{1}{10} \]

4. **Calculate the Image Distance \( v \)**:
Taking the reciprocal gives:
\[ v = 10 \text{ cm} \]

5. **Determine the Sign of \( v \)**:
Since \( v \) is positive, it indicates that the image is formed behind the mirror.

### Final Answer:
The distance of the image from the pole of the mirror is \( 10 \) cm behind the mirror.

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