Question

A glass prism of refracting angle ${60}^o$ gives a minimum deviation of ${30}^o$. what is the refraction index of the glass -

• A. 1.5
• B. $\sqrt{1.5}$
• C. $1/\sqrt{2}$
• D. can not be determined

Answer 1

Answer: (C)

$1/\sqrt{2}$

Given that$,$ $A=60,$ $d=30.$

WE know$,$

$\beta =\left(\frac{\sin \left(\frac{1}{2}\right)\left(a+d\right)}{\sin \frac{1}{2}a}\right)$

implies$,$

$sin(60+30/2)/sin\left(60/2\right)$

implies$,$

$\beta =\sin 45/\sin 30$

$\beta =\sqrt{2}$

implies$,$

$1/\sin i\left(c\right)=\sqrt{2}$

therefore$,$

$\sin i\left(c\right)=1/\sqrt{2}$

Hence,

option $\left(C\right)$ is correct answer.