According to Cartesian sign convention, in ray optics

Options

A. all distances are taken negative
B. all distances in the direction of incident ray are taken positive
C. all distances are taken positive
D. all distances in the direction of incident ray are taken negative

Answer

To solve the question regarding the Cartesian sign convention in ray optics, we need to analyze the options provided and determine which statement is true based on the established conventions in optics.

### Step-by-Step Solution:

1. **Understanding the Cartesian Sign Convention**:
- In ray optics, the Cartesian sign convention is a set of rules used to assign signs to distances measured in ray diagrams. The convention typically states that:
- Distances measured in the direction of the incident ray are considered negative.
- Distances measured in the opposite direction (i.e., the direction of the reflected ray) are considered positive.

2. **Analyzing the Options**:
- **Option A**: "All distances are taken negative."
- This is incorrect because only distances in the direction of the incident ray are negative, while distances in the direction of the reflected ray can be positive.

- **Option B**: "All distances in the direction of incident ray are taken positive."
- This is also incorrect. According to the convention, distances in the direction of the incident ray are negative.

- **Option C**: "All distances are taken positive."
- This is incorrect as well. Distances can be both negative and positive depending on their direction relative to the incident ray.

- **Option D**: "All distances in the direction of incident ray are taken negative."
- This statement is correct. It aligns with the Cartesian sign convention.

3. **Conclusion**:
- The correct answer is **Option D**: "All distances in the direction of incident ray are taken negative."