A prism of crown glass with refracting angle of `5^(@)` and mean refractive index = 1.151 is combined with a flint glass prism of refractive index = 1.65 to produce deviation. Find the angle of fliint glass.

Options

A. `3.92^(@)`
B. `4.68^(@)`
C. `5.32^(@)`
D. `7.28^(@)`

Explanation

To solve the problem, we need to find the angle of the flint glass prism (let's denote it as \( A' \)) that, when combined with a crown glass prism, produces a total deviation equal to that of the crown glass prism alone.

### Step-by-step Solution:

1. **Identify the Given Data:**
- Refracting angle of crown glass prism, \( A = 5^\circ \)
- Mean refractive index of crown glass, \( \mu = 1.51 \)
- Refractive index of flint glass, \( \mu' = 1.65 \)

2. **Calculate the Deviation for Crown Glass Prism:**
The formula for the deviation \( \delta \) produced by a prism is given by:
\[ \delta = (\mu - 1) \cdot A \]
Substituting the values for the crown glass prism:
\[ \delta = (1.51 - 1) \cdot 5^\circ = 0.51 \cdot 5^\circ = 2.55^\circ \]

3. **Set Up the Equation for Flint Glass Prism:**
Let \( A' \) be the angle of the flint glass prism. The deviation \( \delta' \) for the flint glass prism can be expressed as:
\[ \delta' = (\mu' - 1) \cdot A' \]
Substituting the value of \( \mu' \):
\[ \delta' = (1.65 - 1) \cdot A' = 0.65 \cdot A' \]

4. **Equate the Deviations:**
Since the total deviation produced by the combination of both prisms is equal to the deviation produced by the crown glass prism alone, we have:
\[ \delta = \delta' \]
Therefore:
\[ 2.55^\circ = 0.65 \cdot A' \]

5. **Solve for \( A' \):**
Rearranging the equation to find \( A' \):
\[ A' = \frac{2.55^\circ}{0.65} \]
Calculating the value:
\[ A' \approx 3.923^\circ \]

6. **Final Answer:**
Rounding to two decimal places, the angle of the flint glass prism is:
\[ A' \approx 3.92^\circ \]