Question

The least angle of deviation for a glass prism is equal to its refracting angle. The refractive index of glass is 1.5. Then the angle of prism is

• A. $2co{s}^{-1}\left(\frac{3}{4}\right)$
• B. $si{n}^{-1}\left(\frac{3}{4}\right)$
• C. $si{n}^{-1}\left(\frac{3}{2}\right)$
• D. $co{s}^{-1}\left(\frac{3}{2}\right)$

Answer 1

The correct option is A $2co{s}^{-1}\left(\frac{3}{4}\right)$

According to question

$\frac{A+\delta m}{2}$

$\frac{A+A}{2}$

$=A$

$\mu =1.5$

$A=\delta m$

$\mu =\frac{\sin \frac{A+\delta m}{2}}{\sin \frac{A}{2}}$

$\frac{1.5}{1}=\frac{\sin A}{\sin A/2}$

$\frac{3}{2}=\frac{2\sin \frac{A}{2}\cos \frac{A}{2}}{\sin \frac{A}{2}}$

$\cos \frac{A}{2}=\frac{3}{4}$

$A={\cos }^{-1}\frac{3}{4}$