For a glass prism (\( \mu = \sqrt{3} \)), the angle of minimum deviation is equal to the angle of prism. What is the angle of prism?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{\pi}{3} \)
At minimum deviation the ray passes symmetrically through the prism, and the refractive index is given by the prism formula.
\( \displaystyle \mu = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} \)
Putting \( \delta_m = A \):
\( \displaystyle \mu = \frac{\sin A}{\sin(A/2)} = \frac{2\sin(A/2)\cos(A/2)}{\sin(A/2)} = 2\cos\frac{A}{2} \)
\( \displaystyle 2\cos\frac{A}{2} = \sqrt{3} \;\Rightarrow\; \cos\frac{A}{2} = \frac{\sqrt{3}}{2} \;\Rightarrow\; \frac{A}{2} = \frac{\pi}{6} \)
\( \displaystyle A = \frac{\pi}{3} \)
Note: This question is from the NCERT Exemplar. NTA sets numerical questions from the Exemplar too, so do not ignore it while practising numericals.
NCERT Exemplar:
Ray Optics and Optical Instruments – …
