If an object is 40 cm away from a concave mirror of focal length 20 cm, the image will be

Options

A. virtual
B. erect
C. diminished
D. of same size

Answer

To find the characteristics of the image formed by a concave mirror when an object is placed 40 cm away from it, we can use the mirror formula and the properties of concave mirrors. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Object distance (u) = -40 cm (the object distance is taken as negative in mirror convention)
- Focal length (f) = -20 cm (the focal length is negative for concave mirrors)

### Step 2: Use 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 we have:
\[ \frac{1}{-20} = \frac{1}{v} + \frac{1}{-40} \]

### Step 4: Simplify the equation
Rearranging the equation gives:
\[ \frac{1}{v} = \frac{1}{-20} + \frac{1}{40} \]

Finding a common denominator (which is 40):
\[ \frac{1}{v} = \frac{-2}{40} + \frac{1}{40} \]
\[ \frac{1}{v} = \frac{-2 + 1}{40} \]
\[ \frac{1}{v} = \frac{-1}{40} \]

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

### Step 6: Analyze the image characteristics
1. **Image Distance (v)**: The image distance is -40 cm, indicating that the image is formed on the same side as the object.
2. **Real or Virtual**: Since the image distance is negative, the image is real.
3. **Inverted or Erect**: The image formed by a concave mirror is inverted.
4. **Size of the Image**: The object is at the center of curvature (C), and since the object distance is equal to the radius of curvature, the image will be of the same size as the object.

### Conclusion
The image formed is:
- Real
- Inverted
- Of the same size as the object