Question

For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index:

• A. lies between √(2) and 1
• B. lies between 2 and √(2)
• C. is less than 1
• D. is greater than 2

Hint:

For prism problems: μ=(sin((A+δ)/(2)))/(sin((A)/(2))) Special conditions simplify this greatly.

Answer 1

The Correct Option is B

Step 1: Prism formula at minimum deviation:
\( \mu = \dfrac{\sin\left(\dfrac{A+\delta}{2}\right)}{\sin\left(\dfrac{A}{2}\right)} \)
Step 2: Given \( \delta = A \):
\( \mu = \dfrac{\sin A}{\sin\left(\dfrac{A}{2}\right)} = 2\cos\left(\dfrac{A}{2}\right) \)
Step 3: Since \( 0 < A < 90^\circ \),
\( \cos\left(\dfrac{A}{2}\right) \) lies between \( \dfrac{1}{\sqrt{2}} \) and \( 1 \)
Step 4:
\( \mu = 2\cos\left(\dfrac{A}{2}\right) \Rightarrow \sqrt{2} < \mu < 2 \)