Which of the following graph represents relation between the image position (v) and object position (u) from the concave lens.

Options

A.
B.
C.
D.

Answer

To determine the relationship between the image position (v) and object position (u) for a concave lens, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Lens Formula**:
The lens formula is given by:
\[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \]
For a concave lens, the focal length (f) is negative.

2. **Identify the Sign Conventions**:
- Object distance (u) is negative when the object is on the same side as the incoming light (which is the case for a concave lens).
- Image distance (v) is also negative for virtual images formed by concave lenses.

3. **Analyze Different Object Positions**:
- **When u = -∞**: The image forms at v = -f (which is a finite distance on the same side as the object).
- **When u = 0**: The image also forms at the origin (v = 0).
- **When u = -f**: The image will be at v = -∞ (the image moves infinitely far away).
- **When u = -2f**: The image will be at v = -2f (still on the same side as the object but at a finite distance).

4. **Plot the Points**:
- Plot the points on a graph where:
- For \( u = -\infty \), \( v = -f \)
- For \( u = 0 \), \( v = 0 \)
- For \( u = -f \), \( v = -\infty \)
- For \( u = -2f \), \( v = -2f \)

5. **Draw the Curve**:
- Connect the points smoothly to represent the relationship. The graph will start from \( (-\infty, -f) \) and curve towards \( (0, 0) \), then continue to \( (-2f, -2f) \) and approach \( (-\infty, -f) \).

6. **Identify the Correct Graph**:
- Compare the drawn curve with the provided options to identify which graph accurately represents the relationship between image position (v) and object position (u) for a concave lens.