A ray of light is incident on one of the faces of the angle prism with an angle `40^(@)` with the surface. The angle of the prism is `60^(@)`. The emergent ray is deviated through an angle `38^(@)`. The angle of emergence is

Options

A. `38^(@)`
B. `48^(@)`
C. `52^(@)`
D. `58^(@)`

Answer

To solve the problem step by step, we will follow the principles of ray optics related to prisms.

### Step 1: Understand the given information
- Angle of incidence (i) with respect to the normal: Since the ray makes an angle of 40° with the surface, the angle of incidence (i) with respect to the normal is:
\[ i = 90° - 40° = 50° \]
- Angle of the prism (A): Given as 60°.
- Angle of deviation (δ): Given as 38°.

### Step 2: Use the formula for angle of deviation
The formula relating the angle of incidence (i), angle of emergence (e), and angle of the prism (A) is given by:
\[ \delta = i + e - A \]
Where:
- δ = angle of deviation
- i = angle of incidence
- e = angle of emergence
- A = angle of the prism

### Step 3: Substitute the known values into the formula
We can substitute the known values into the formula:
\[ 38° = 50° + e - 60° \]

### Step 4: Rearrange the equation to solve for the angle of emergence (e)
Rearranging the equation gives:
\[ e = \delta + A - i \]
Substituting the values:
\[ e = 38° + 60° - 50° \]

### Step 5: Calculate the angle of emergence
Now, calculate the angle of emergence:
\[ e = 38° + 60° - 50° = 48° \]

### Conclusion
The angle of emergence (e) is:
\[ \boxed{48°} \]