Question

Critical angle for a light ray travelling from denser to rarer medium is defined as the angle of incidence at which the angle of refraction is 90°.
If a ray of light travels from water $\left({\mu }_w\right)$ to air $\left({\mu }_a\right)$. Find the critical angle?

• A. ${\sin }^{-1}\left(\frac{{\mu }_w}{{\mu }_a}\right)$
• B. ${\sin }^{-1}\left(\frac{{\mu }_a}{{\mu }_w}\right)$
• C. ${\cos }^{-1}\left(\frac{{\mu }_w}{{\mu }_a}\right)$
• D. ${90}^{\circ }$

Answer 1

The correct option is B

${\sin }^{-1}\left(\frac{{\mu }_a}{{\mu }_w}\right)$

Applying Snell's law at interface:
${\mu }_w\sin i_c={\mu }_a\sin \left({90}^{\circ }\right)$
$i_c$ = ${\sin }^{-1}\left(\frac{{\mu }_a}{{\mu }_w}\right)$