A ray of light is inclined to one face of a prism at an angle of `50^@`. The angle of prism is `60^@` and the ray deviates through an angle which the emergent ray makes with second face of the prism.

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the given information
- The angle of incidence (i) with the first face of the prism is given as \(50^\circ\).
- The angle of the prism (A) is \(60^\circ\).
- The angle of deviation (\(\delta\)) is \(42^\circ\).

### Step 2: Calculate the angle of incidence (i)
The angle of incidence (i) is measured from the normal to the surface. Since the ray is inclined at \(50^\circ\) to the face of the prism, we can find the angle of incidence using the relation:
\[ i = 90^\circ - 50^\circ = 40^\circ \]

### Step 3: Use the formula for angle of deviation
The angle of deviation (\(\delta\)) can be expressed using the formula:
\[ \delta = i + e - A \]
Where:
- \(e\) is the angle of emergence,
- \(A\) is the angle of the prism.

Substituting the known values into the equation:
\[ 42^\circ = 40^\circ + e - 60^\circ \]

### Step 4: Solve for the angle of emergence (e)
Rearranging the equation to solve for \(e\):
\[ 42^\circ = 40^\circ + e - 60^\circ \]
\[ 42^\circ = e - 20^\circ \]
\[ e = 42^\circ + 20^\circ = 62^\circ \]

### Step 5: Calculate the angle the emergent ray makes with the second face of the prism
The angle that the emergent ray makes with the second face of the prism (\(\theta\)) can be found using:
\[ \theta = 90^\circ - e \]
Substituting the value of \(e\):
\[ \theta = 90^\circ - 62^\circ = 28^\circ \]

### Final Answer
The emergent ray makes an angle of \(28^\circ\) with the second face of the prism.

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