A flint glass prism and a crown glass prism are to be comblined in such a way that the deviation of the mean ray is zero. The refractive index of the flint glass for the mean ray is `1.62` and for the crown glass it is `1.518`. If the angle of the flint glass prism is `6^(@)`, what would be refracting angle of the

Answer

To solve the problem of combining a flint glass prism and a crown glass prism so that the deviation of the mean ray is zero, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Refractive index of flint glass, \( n_f = 1.62 \)
- Refractive index of crown glass, \( n_c = 1.518 \)
- Angle of the flint glass prism, \( A_f = 6^\circ \)

2. **Understand the Condition for Zero Deviation:**
- For the mean ray to have zero deviation, the deviation caused by the flint glass prism must be equal and opposite to the deviation caused by the crown glass prism.

3. **Use the Deviation Formula:**
- The formula for the deviation \( D \) caused by a prism is given by:
\[ D = (n - 1)A \]
- Therefore, for the flint glass prism:
\[ D_f = (n_f - 1)A_f \]
- And for the crown glass prism:
\[ D_c = (n_c - 1)A_c \]

4. **Set the Deviations Equal:**
- Since \( D_f + D_c = 0 \), we can write:
\[ D_f = D_c \]
- Substituting the deviation formulas, we have:
\[ (n_f - 1)A_f = (n_c - 1)A_c \]

5. **Rearranging the Equation:**
- We can express \( A_c \) in terms of \( A_f \):
\[ A_c = \frac{(n_f - 1)}{(n_c - 1)} A_f \]

6. **Substituting the Values:**
- Plugging in the values:
\[ A_c = \frac{(1.62 - 1)}{(1.518 - 1)} \times 6^\circ \]
- This simplifies to:
\[ A_c = \frac{0.62}{0.518} \times 6^\circ \]

7. **Calculating the Angle \( A_c \):**
- Performing the division:
\[ A_c \approx 1.196 \times 6^\circ \approx 7.176^\circ \]
- Rounding to one decimal place gives:
\[ A_c \approx 7.2^\circ \]

### Final Answer:
The refracting angle of the crown glass prism is approximately \( 7.2^\circ \).