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

Options

A. 13.3 cm
B. 20 cm
C. 25 cm
D. 10 cm

Answer

To solve the problem of finding the image distance produced by a convex mirror when an object is placed at a distance of 20 cm from its pole, we will use the mirror formula. Here’s a step-by-step solution:

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

### Step 2: Write 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

### Step 3: Substitute the known values into the mirror formula
Substituting the values into the formula:
\[ \frac{1}{20} = \frac{1}{v} + \frac{1}{-20} \]

### Step 4: Simplify the equation
Rearranging the equation gives:
\[ \frac{1}{20} + \frac{1}{20} = \frac{1}{v} \]
This simplifies to:
\[ \frac{2}{20} = \frac{1}{v} \]

### Step 5: Solve for \( v \)
Taking the reciprocal of both sides:
\[ v = \frac{20}{2} = 10 \text{ cm} \]

### Conclusion
The image is produced at a distance of 10 cm from the pole of the convex mirror.