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

### Step-by-Step Solution:

1. **Identify the given values:**
- Focal length of the convex mirror (f) = +10 cm (positive for convex mirrors)
- Object distance (u) = -20 cm (negative as per the sign convention for mirrors)

2. **Use the mirror formula:**
The mirror formula is given by:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
Substituting the known values into the formula:
\[ \frac{1}{10} = \frac{1}{v} + \frac{1}{-20} \]

3. **Rearranging the equation:**
\[ \frac{1}{v} = \frac{1}{10} + \frac{1}{20} \]
To add the fractions, find a common denominator (which is 20):
\[ \frac{1}{10} = \frac{2}{20} \]
So,
\[ \frac{1}{v} = \frac{2}{20} - \frac{1}{20} = \frac{1}{20} \]

4. **Calculate v:**
Taking the reciprocal gives:
\[ v = 20 \text{ cm} \]
(The positive sign indicates that the image is virtual and located on the same side as the object.)

5. **Calculate the magnification (m):**
The magnification formula is given by:
\[ m = -\frac{v}{u} \]
Substituting the values:
\[ m = -\frac{20}{-20} = 1 \]

6. **Interpret the results:**
- The image distance (v) is +20 cm, indicating that the image is virtual and located 20 cm behind the mirror.
- The magnification (m) is 1, which means the image size is the same as the object size.

### Conclusion:
The image formed by the convex mirror is virtual, located 20 cm behind the mirror, and has the same size as the object.