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 will use the formula for the angle of deviation produced by a prism. The angle of deviation (Δ) for a prism can be expressed as:

\[ \Delta = (n - 1)A \]

where:
- \( n \) is the refractive index of the prism,
- \( A \) is the refracting angle of the prism.

Given:
- For the crown glass prism:
- Refracting angle \( A = 5^\circ \)
- Mean refractive index \( n = 1.151 \)

- For the flint glass prism:
- Refractive index \( n' = 1.65 \)
- Let the refracting angle be \( A' \) (which we need to find).

### Step 1: Calculate the angle of deviation for the crown glass prism.

Using the formula:

\[ \Delta = (n - 1)A \]

Substituting the values for the crown glass prism:

\[ \Delta = (1.151 - 1) \times 5 \]

\[ \Delta = 0.151 \times 5 \]

\[ \Delta = 0.755 \text{ degrees} \]

### Step 2: Set the angle of deviation for the flint glass prism equal to that of the crown glass prism.

Since the total deviation produced by both prisms is the same, we have:

\[ \Delta = (n' - 1)A' \]

Substituting the values for the flint glass prism:

\[ 0.755 = (1.65 - 1)A' \]

\[ 0.755 = 0.65A' \]

### Step 3: Solve for \( A' \).

Rearranging the equation gives:

\[ A' = \frac{0.755}{0.65} \]

Calculating this:

\[ A' = 1.1615 \text{ degrees} \]

### Step 4: Convert to degrees.

To express this in degrees, we can round it:

\[ A' \approx 1.16 \text{ degrees} \]

### Conclusion

The angle of the flint glass prism is approximately \( 1.16^\circ \).

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