A ray of light is incident at an angle of `50^(@)` on one face of an equilateral prism . What is the angle ,which the emergent ray makes with the second face of the prism , if the deviation produced by the prism is `42^(@) ` ?

Options

A. `48^(@)`
B. `38^(@)`
C. `58^(@)`
D. `42^(@)`

Explanation

To solve the problem step by step, we will use the given information about the prism and apply the relevant formulas.

### Step 1: Identify the Given Data
- Angle of incidence (I) = 50°
- Angle of prism (A) = 60° (since it is an equilateral prism)
- Angle of deviation (Δ) = 42°

### Step 2: Use the Relation Between Angles
In a prism, the relationship between the angle of incidence (I), angle of emergence (E), angle of prism (A), and angle of deviation (Δ) is given by the formula:
\[ I + E = A + Δ \]

### Step 3: Substitute the Known Values
Now, we can substitute the known values into the equation:
\[ 50° + E = 60° + 42° \]

### Step 4: Simplify the Equation
Calculate the right side:
\[ 50° + E = 102° \]

### Step 5: Solve for the Angle of Emergence (E)
Now, isolate E:
\[ E = 102° - 50° \]
\[ E = 52° \]

### Step 6: Find the Angle with the Second Face
The angle of emergence (E) is measured with respect to the normal at the second face of the prism. To find the angle that the emergent ray makes with the second face of the prism, we need to subtract E from 90°:
\[ \text{Angle with second face} = 90° - E \]
\[ \text{Angle with second face} = 90° - 52° \]
\[ \text{Angle with second face} = 38° \]

### Final Answer
The angle which the emergent ray makes with the second face of the prism is **38°**.

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