In a thin prism of glass (refractive index 1.5), which of the following relations between the angle of minimum deviations `delta_(m)` and angle of prism r will be correct?

Options

A. `delta_(m)=r`
B. `delta_(m)=1.5r`
C. `delta_(m)=2r`
D. `delta_(m)=r/2`

Explanation

To find the relationship between the angle of minimum deviation (δ_m) and the angle of the prism (r) for a thin prism of glass with a refractive index (μ) of 1.5, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Variables**:
- Let the angle of the prism be denoted as \( r \).
- Let the angle of minimum deviation be denoted as \( \delta_m \).
- The refractive index of the glass prism is given as \( \mu = 1.5 \).

2. **Use the Formula for Minimum Deviation**:
- The relationship between the angle of minimum deviation and the angle of the prism is given by the formula:
\[ \delta_m = (\mu - 1) \cdot r \]

3. **Substitute the Values**:
- Substitute the value of \( \mu \) into the equation:
\[ \delta_m = (1.5 - 1) \cdot r \]
- Simplifying this gives:
\[ \delta_m = 0.5 \cdot r \]

4. **Consider the Condition for Minimum Deviation**:
- In the case of minimum deviation, the angle of the prism \( r \) is related to the angle \( a \) (angle of the prism) as:
\[ r = \frac{a}{2} \]
- Therefore, we can express \( a \) in terms of \( r \):
\[ a = 2r \]

5. **Substitute \( a \) Back into the Formula**:
- Now, substitute \( a = 2r \) back into the equation for minimum deviation:
\[ \delta_m = 0.5 \cdot (2r) \]
- This simplifies to:
\[ \delta_m = r \]

6. **Conclusion**:
- The relationship between the angle of minimum deviation and the angle of the prism is:
\[ \delta_m = r \]

### Final Answer:
The correct relation between the angle of minimum deviation \( \delta_m \) and the angle of the prism \( r \) is:
\[ \delta_m = r \]