An object is placed at 20 cm from a convex mirror of focal length 10 cm. The image formed by a mirror is

Options

A. Real and at 20 cm from the mirror
B. Virtual and at 20 cm from the mirror
C. Virtual and at 20/3 cm from the mirror
D. Real and at 20/3 cm from the mirror

Answer

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

### Step-by-Step Solution:

1. **Identify Given Values**:
- Object distance (u) = -20 cm (the negative sign indicates that the object is placed in front of the mirror).
- Focal length (f) = +10 cm (the positive sign indicates that it is a convex 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,
- \( v \) is the image distance,
- \( u \) is the object distance.

3. **Substitute the Known Values**:
Substitute \( f = 10 \) cm and \( u = -20 \) cm into the mirror formula:
\[ \frac{1}{10} = \frac{1}{v} + \frac{1}{-20} \]

4. **Rearrange the Equation**:
Rearranging gives:
\[ \frac{1}{v} = \frac{1}{10} + \frac{1}{20} \]

5. **Find a Common Denominator**:
The common denominator for 10 and 20 is 20. Thus:
\[ \frac{1}{10} = \frac{2}{20} \]
Therefore:
\[ \frac{1}{v} = \frac{2}{20} + \frac{1}{20} = \frac{3}{20} \]

6. **Calculate Image Distance (v)**:
Now, take the reciprocal to find \( v \):
\[ v = \frac{20}{3} \text{ cm} \approx 6.67 \text{ cm} \]

7. **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 means it is a virtual image.

### Final Answer:
The image formed by the convex mirror is located at approximately 6.67 cm behind the mirror, and it is a virtual image.

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