An object is placed at a distance of 20 cm from the pole of a concave mirror of focal length 10 cm. The distance of the image formed is

Options

A. `+20 cm`
B. `+10Cm`
C. `-20 cm`
D. `-10cm`

Answer

To solve the problem of finding the distance of the image formed by a concave mirror, we will use the mirror formula:

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

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

### Step 1: Identify the given values
- The object distance \( u = -20 \) cm (negative because the object is in front of the mirror).
- The focal length \( f = -10 \) cm (negative for concave mirrors).

### Step 2: Substitute the values into the mirror formula
Using the mirror formula:

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

Substituting the known values:

\[ \frac{1}{-10} = \frac{1}{v} + \frac{1}{-20} \]

### Step 3: Rearranging the equation
Rearranging the equation gives:

\[ \frac{1}{v} = \frac{1}{-10} + \frac{1}{20} \]

### Step 4: Finding a common denominator
The common denominator for -10 and 20 is 20. Thus, we rewrite the fractions:

\[ \frac{1}{v} = \frac{-2}{20} + \frac{1}{20} \]

### Step 5: Simplifying the equation
Now, combine the fractions:

\[ \frac{1}{v} = \frac{-2 + 1}{20} = \frac{-1}{20} \]

### Step 6: Solve for \( v \)
Taking the reciprocal gives:

\[ v = -20 \text{ cm} \]

### Conclusion
The distance of the image formed is \( -20 \) cm, which indicates that the image is formed on the same side as the object.