In an experiment for determination of refractive index of glass of a prism by `i-delta`, plot it was found thata ray incident at angle `35^circ`, suffers a deviation of `40^circ` and that it emerges at angle `79^circ`. In that case which of the following is closest to the maximum possible value of the refractive index?

Options

A. 1.6
B. 1.7
C. 1.8
D. 1.5

Answer

To solve the problem of determining the maximum possible value of the refractive index of a glass prism based on the given angles, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Values**:
- Angle of incidence (I) = 35°
- Angle of emergence (E) = 79°
- Angle of deviation (Δ) = 40°

2. **Use the Deviation Formula**:
The formula for deviation (Δ) in a prism is given by:
\[ Δ = I + E - A \]
where A is the angle of the prism.

3. **Rearranging the Deviation Formula**:
We can rearrange the formula to find the angle of the prism (A):
\[ A = I + E - Δ \]

4. **Substituting the Values**:
Plugging in the values we have:
\[ A = 35° + 79° - 40° \]
\[ A = 114° - 40° = 74° \]

5. **Finding the Refractive Index (μ)**:
The maximum possible value of the refractive index (μ) for a prism can be calculated using the formula:
\[ μ = \frac{\sin\left(\frac{A + I}{2}\right)}{\sin\left(\frac{A}{2}\right)} \]

6. **Calculating the Angles**:
First, calculate \( \frac{A + I}{2} \) and \( \frac{A}{2} \):
- \( A + I = 74° + 35° = 109° \)
- \( \frac{A + I}{2} = \frac{109°}{2} = 54.5° \)
- \( \frac{A}{2} = \frac{74°}{2} = 37° \)

7. **Calculating the Sine Values**:
Now, we calculate the sine values:
- \( \sin(54.5°) \)
- \( \sin(37°) \)

Using a calculator or sine tables:
- \( \sin(54.5°) \approx 0.8192 \)
- \( \sin(37°) \approx 0.6018 \)

8. **Substituting into the Refractive Index Formula**:
Now substitute these values into the refractive index formula:
\[ μ = \frac{0.8192}{0.6018} \approx 1.36 \]

9. **Conclusion**:
The maximum possible value of the refractive index is approximately 1.36. The closest option to this value is 1.4.

### Final Answer:
The closest maximum possible value of the refractive index is **1.4**.