Question

Refractive index of a medium is $\mu$. The incidence angle is twice that of refracting angle. The angle of incidence is :

• A. ${cos}^{-1}\left(\frac{\mu }{2}\right)$
• B. ${sin}^{-1}\left(\frac{\mu }{2}\right)$
• C. ${2cos}^{-1}\left(\frac{\mu }{2}\right)$
• D. ${sin}^{-1}\mu$

Answer 1

The correct option is C ${2cos}^{-1}\left(\frac{\mu }{2}\right)$

The correct answer is (C).

Given,

The refractive index of the medium is $\mu$

The angle of incidence is $i=2r$

Apply the Snell’s law

${\mu }_1\sin i={\mu }_2\sin r$

Where ${\mu }_1=1$, ${\mu }_2=\mu$, and $i=2r$

$\sin 2r=\mu \sin r$

$2\sin r\cos r=\mu \sin r$

$2\cos r=\mu \Rightarrow r={\cos }^{-1}\left(\frac{\mu }{2}\right)$

Hence the angle of incidence $i=2r=2{\cos }^{-1}\left(\frac{\mu }{2}\right)$ .