For a given prism `thetaanddelta` are angular dispersion and deviation. Correct relation is

Options

A. `thetapropdelta`
B. `thetaprop1/delta`
C. `thetapropdelta^(2)`
D. `thetaalphaprop1/delta^(2)`

Answer

To find the correct relation between angular dispersion (θ) and angular deviation (δ) for a given prism, we can follow these steps:

### Step 1: Understand the Definitions
- **Angular Deviation (δ)**: This is the angle by which a ray of light is deviated from its original path after passing through the prism. It can be represented as the mean deviation of the rays passing through the prism.
- **Angular Dispersion (θ)**: This is the difference in deviation between the colors (or wavelengths) of light as they pass through the prism. It is calculated as the difference between the maximum deviation (for violet light, δv) and the minimum deviation (for red light, δr).

### Step 2: Write the Formula for Angular Dispersion
The formula for angular dispersion can be expressed as:
\[ θ = δv - δr \]
where:
- δv = deviation for violet light
- δr = deviation for red light

### Step 3: Relate Angular Deviation to Mean Deviation
The mean deviation (δ) can be considered as the deviation for a specific color, often taken as the yellow light (or the mean of the visible spectrum). Thus, we can express the mean deviation as:
\[ δ = \text{mean deviation (for a specific color)} \]

### Step 4: Establish the Relationship
Since the dispersive power (ω) of the prism is defined as the ratio of angular dispersion to angular deviation, we can write:
\[ ω = \frac{θ}{δ} \]
Given that the dispersive power is constant for a specific prism, we can rearrange this to show:
\[ θ = ω \cdot δ \]
This indicates that angular dispersion (θ) is directly proportional to angular deviation (δ).

### Conclusion
Thus, the correct relation between angular dispersion (θ) and angular deviation (δ) for a given prism is:
\[ θ \propto δ \]