An object is at 20 cm from a concave mirror of focal length 10 cm, the nature of image is

Options

A. Real and inverted
B. Virtual and erect
C. Real and 3 times magnified
D. Real and 2 times magnified

Answer

To determine the nature of the image formed by a concave mirror when an object is placed at a distance of 20 cm from the mirror, we can use the mirror formula and the concept of magnification. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Object distance (u) = -20 cm (the negative sign indicates that the object is in front of the mirror)
- Focal length (f) = -10 cm (the negative sign indicates that it is a concave mirror)

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

### Step 3: Rearrange the equation
Rearranging the equation gives:
\[ \frac{1}{v} = \frac{1}{-10} + \frac{1}{20} \]

### Step 4: Find a common denominator and simplify
The common denominator for -10 and 20 is 20. Thus, we can rewrite the equation as:
\[ \frac{1}{v} = \frac{-2}{20} + \frac{1}{20} = \frac{-2 + 1}{20} = \frac{-1}{20} \]

### Step 5: Solve for v
Taking the reciprocal gives:
\[ v = -20 \text{ cm} \]
The negative sign indicates that the image is formed on the same side as the object.

### Step 6: Determine the nature of the image
Since the image distance (v) is negative, the image is real and located on the same side as the object.

### Step 7: Determine the size and orientation of the image
To find the magnification (m), we use the magnification formula:
\[ m = \frac{H_i}{H_o} = -\frac{v}{u} \]
Substituting the values:
\[ m = -\frac{-20}{-20} = -1 \]
This means the image is of the same size as the object and inverted.

### Conclusion
The nature of the image is:
- Real
- Inverted
- Same size as the object