Question

A ray of light passes from vacuum into a medium of refractive index $\mu$. If the angle of incidence is found to be twice the angle of refraction, then the angle of incidence is:($\text{sin}2r=2\text{sin}r\text{cos}r$)

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

Answer 1

The correct option is B

$2{\text{cos}}^{-1}\left(\frac{\mu }{2}\right)$

According to Snell's law

$\frac{\text{sin}\left(i\right)}{\text{sin}\left(r\right)}=\frac{{\mu }_2}{{\mu }_1}$

By using $\mu =\frac{\text{sin}i}{\text{sin}r}\Rightarrow \mu =\frac{\text{sin}2r}{\text{sin}r}=\frac{2\text{sin}r\text{cos}r}{\text{sin}r}$
$\Rightarrow r={\text{cos}}^{-1}\left(\frac{\mu }{2}\right).So,i=2r=2{\text{cos}}^{-1}\left(\frac{\mu }{2}\right)$