An object is placed 40 cm from a concave mirror of focal length 20 cm. The image formed is

Options

A. real,inverted and same in size
B. real,inverted and smaller in size
C. virtual,erect and larger in size
D. virtual,erect and smaller in size

Explanation

To solve the problem of finding the characteristics of the image formed by a concave mirror when an object is placed at a certain distance, we will follow these steps:

### Step 1: Identify the given values
- Object distance (u) = -40 cm (the negative sign indicates that the object is in front of the mirror)
- Focal length (f) = -20 cm (the negative sign indicates that it is a concave mirror)

### Step 2: Use the mirror formula
The mirror formula is given by:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
Rearranging the formula to find the image distance (v):
\[ \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \]

### Step 3: Substitute the values into the formula
Substituting the values of f and u:
\[ \frac{1}{v} = \frac{1}{-20} - \frac{1}{-40} \]
This simplifies to:
\[ \frac{1}{v} = -\frac{1}{20} + \frac{1}{40} \]

### Step 4: Find a common denominator and simplify
The common denominator for 20 and 40 is 40. Therefore:
\[ \frac{1}{v} = -\frac{2}{40} + \frac{1}{40} = -\frac{2 - 1}{40} = -\frac{1}{40} \]

### Step 5: Solve for v
Taking the reciprocal gives:
\[ v = -40 \text{ cm} \]

### Step 6: Determine the characteristics of the image
1. The negative sign of v indicates that the image is formed on the same side as the object, which means it is a real image.
2. To find the magnification (m), we use the formula:
\[ m = -\frac{v}{u} \]
Substituting the values:
\[ m = -\frac{-40}{-40} = -1 \]
The negative sign indicates that the image is inverted, and the magnitude of 1 indicates that the size of the image is the same as that of the object.

### Conclusion
The image formed is real, inverted, and of the same size as the object.