The object or image distance is taken as positive

Options

A. if the length is measured opposite to the direction of the incident ray.
B. if the length is measured in the direction of the incident ray.
C. if the length is measured opposite to the direction of the refracted ray.
D. None of these

Answer

To solve the question regarding the sign convention for object and image distances in optics, we need to analyze the options provided based on the behavior of light rays. Here’s a step-by-step breakdown of the solution:

### Step-by-Step Solution:

1. **Understanding the Sign Convention**:
- In optics, the sign convention is crucial for determining whether the distances are positive or negative. The direction of the incident ray is the key factor in this convention.

2. **Identify the Direction of the Incident Ray**:
- The incident ray is the ray that approaches the mirror or lens. We need to establish which direction this ray is coming from to determine our positive and negative distances.

3. **Positive Distance**:
- According to the sign convention, the distance is considered positive if it is measured in the same direction as the incident ray. This means that if you measure a distance in the direction the ray is coming from, it will be positive.

4. **Negative Distance**:
- Conversely, if the distance is measured opposite to the direction of the incident ray, it will be considered negative. Therefore, if you measure in the opposite direction of where the incident ray is coming from, that distance is negative.

5. **Analyzing the Options**:
- **Option 1**: "The object or image distance is taken as positive if the length is measured opposite to the direction of the incident ray."
- This is incorrect because distances measured opposite to the incident ray are negative.

- **Option 2**: "The object or image distance is taken as positive if the length is measured in the direction of the incident ray."
- This is correct because distances measured in the direction of the incident ray are positive.

- **Option 3**: "The object or image distance is taken as positive if the length is measured opposite to the direction of the reflected ray."
- This is incorrect because the sign convention is based on the incident ray, not the reflected ray.

- **Option 4**: "None of them."
- This is incorrect because we have already established that Option 2 is correct.

6. **Conclusion**:
- The correct answer is **Option 2**: "The object or image distance is taken as positive if the length is measured in the direction of the incident ray."