Question

If angle of incidence is twice the angle of refraction in a medium index $\mu$, the angle of incidence is

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

Answer 1

The correct option is A $2{\cos }^{-1}\frac{\mu }{2}$

according to Snell's law
Refractive index, $\mu =\frac{\sin i}{\sin r}$
Given $i=2r$
$\therefore \mu =\frac{\sin 2r}{\sin r}$
or $\mu =\frac{2\sin r\cos r}{\sin r}$
or ${\cos }^{-1}\frac{\mu }{2}=r$
$\Rightarrow i=2{\cos }^{-1}\frac{\mu }{2}$