A crown glass prism and a flint glass prism are combined to produce dispersion without deviation. Mean refractive indices of crown , and flint glass are respectively 1.5 and 1.6. Ratio of angle of crown glass prism to that of flint prism is

Options

A. 1.06
B. 0.9375
C. 1.2
D. 1.5

Explanation

To solve the problem of finding the ratio of the angle of the crown glass prism to that of the flint glass prism, we will use the formula for dispersion without deviation.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- Refractive index of crown glass (Ic) = 1.5
- Refractive index of flint glass (If) = 1.6

2. **Use the Formula for Dispersion Without Deviation**:
The condition for dispersion without deviation can be expressed as:
\[ \theta_f \cdot (I_f - 1) = \theta_c \cdot (I_c - 1) \]
where:
- \(\theta_f\) = angle of the flint glass prism
- \(\theta_c\) = angle of the crown glass prism

3. **Rearranging the Formula**:
We can rearrange the formula to find the ratio of the angles:
\[ \frac{\theta_c}{\theta_f} = \frac{I_f - 1}{I_c - 1} \]

4. **Substituting the Values**:
Substitute the refractive indices into the equation:
\[ \frac{\theta_c}{\theta_f} = \frac{1.6 - 1}{1.5 - 1} = \frac{0.6}{0.5} \]

5. **Calculating the Ratio**:
Simplifying the fraction gives:
\[ \frac{\theta_c}{\theta_f} = \frac{0.6}{0.5} = 1.2 \]

6. **Conclusion**:
The ratio of the angle of the crown glass prism to that of the flint glass prism is:
\[ \frac{\theta_c}{\theta_f} = 1.2 \]

### Final Answer:
The ratio of the angle of the crown glass prism to that of the flint glass prism is **1.2**.