A concave lens always produces ……………………………. images.

Options

A. Real
B. virtual
C. magnified
D. None of these

Answer

To determine the type of images produced by a concave lens, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Lens Type**: A concave lens is a diverging lens, meaning it spreads out light rays that are initially parallel to its principal axis.

2. **Object Placement**: Let's assume an object is placed in front of the concave lens. The distance of the object from the lens is denoted as 'u'. For lens formula calculations, this distance is considered negative (u = -u₀) because it is measured against the direction of the incoming light.

3. **Focal Length**: The focal length (f) of a concave lens is also negative (f = -f). This is important for applying the lens formula.

4. **Lens Formula**: The lens formula is given by:
\[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \]
Rearranging this gives:
\[ \frac{1}{v} = \frac{1}{f} + \frac{1}{u} \]

5. **Substituting Values**: Substituting the values of 'u' and 'f' into the lens formula:
\[ \frac{1}{v} = \frac{1}{-f} + \frac{1}{-u₀} = -\frac{1}{f} - \frac{1}{u₀} \]
This will yield a negative value for 'v', indicating that the image is virtual.

6. **Magnification Calculation**: The magnification (M) of the lens is given by:
\[ M = \frac{v}{u} \]
Since 'v' is negative and 'u' is also negative, the magnification will be positive. This indicates that the image is upright.

7. **Image Characteristics**: From the above calculations, we can conclude that:
- The image formed by a concave lens is virtual (since 'v' is negative).
- The image is upright (since magnification is positive).
- The image is diminished (since the absolute value of magnification is less than 1).

### Final Answer:
A concave lens always produces **virtual** images.