Question

What will be the refractive index of a thin prism material if its refracting angle and angle of deviation are the same?

• A. 1.5
• B. 2.0
• C. 1.33
• D. 0 (zero)

Hint:

The refractive index of a thin prism can be determined using the relationship between the refracting angle and the angle of deviation.

Answer 1

The Correct Option is C

Step 1: Understanding the Relationship Between Refracting Angle and Deviation.
For a thin prism, the angle of deviation \( \delta \) is related to the refracting angle \( A \) and the refractive index \( n \) by the formula: \[ \delta = (n - 1)A \] In the case where the refracting angle \( A \) and the angle of deviation \( \delta \) are equal, we set \( \delta = A \), thus: \[ A = (n - 1)A \]
Step 2: Solving for Refractive Index.
Canceling \( A \) from both sides (assuming \( A \neq 0 \)), we get: \[ 1 = n - 1 \] Solving for \( n \), we get: \[ n = 2 \]
Step 3: Conclusion.
The refractive index of the thin prism material is \( n = 2 \), making option (B) the correct answer.