Question

If \( r_1 \) and \( r_2 \) are the angles of refraction at the first face and second face of a prism, then the angle of the prism is:

• A. \( r_1 - r_2 \)
• B. \( \frac{r_1 - r_2}{2} \)
• C. \( \frac{r_1 + r_2}{2} \)
• D. \( r_1 + r_2 \)

Hint:

In a prism, the total angle of the prism is equal to the sum of the angles of refraction at the two faces. This is a key concept for solving problems involving prisms.

Answer 1

The Correct Option is D

Step 1: Understand the relation for the angle of the prism.
In a prism, the total angle of the prism \( A \) is related to the angles of refraction \( r_1 \) and \( r_2 \) at the two faces of the prism. The formula to calculate the angle of the prism is: \[ A = r_1 + r_2 \] Where:
\( r_1 \) is the angle of refraction at the first face of the prism,
\( r_2 \) is the angle of refraction at the second face of the prism.

Step 2: Apply the formula.
Thus, the angle of the prism is the sum of the angles of refraction at both the faces of the prism. Final Answer: The correct answer is \( r_1 + r_2 \).