A ray incident a `15^(@)` on one refracting surface of a prism of angle `60^(@)` , suffers a deviation of `55^(@)` . What is the angle of emergence

Options

A. `95^(@)`
B. `45^(@)`
C. `30^(@)`
D. None of these

Answer

To solve the problem, we need to find the angle of emergence of a ray passing through a prism. We are given the following information:

- Angle of incidence (i) = 15°
- Angle of the prism (A) = 60°
- Angle of deviation (δ) = 55°

We can use the formula that relates these angles in a prism:

\[ i + e = A + δ \]

Where:
- \( i \) is the angle of incidence,
- \( e \) is the angle of emergence,
- \( A \) is the angle of the prism,
- \( δ \) is the angle of deviation.

### Step-by-Step Solution:

1. **Write down the known values:**
- Angle of incidence (i) = 15°
- Angle of the prism (A) = 60°
- Angle of deviation (δ) = 55°

2. **Substitute the known values into the formula:**
\[ i + e = A + δ \]
\[ 15° + e = 60° + 55° \]

3. **Calculate the right side of the equation:**
\[ 60° + 55° = 115° \]
So, the equation becomes:
\[ 15° + e = 115° \]

4. **Solve for the angle of emergence (e):**
\[ e = 115° - 15° \]
\[ e = 100° \]

### Final Answer:
The angle of emergence (e) is **100°**.