Question

If a ray of light travels from water (μ_w) to air (μ_a). Find the critical angle?

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

Answer 1

The correct option is B

${\sin }^{-1}$ $\frac{{\mu }_a}{{\mu }_w}$

When angle of incidence is equal to critical angle, angle of refraction is 90 degree.
Apply Snell's law at interface

${\mu }_w$ sin $i_c$ = ${\mu }_a$ sin ${90}^{\circ }$ , where sin ${90}^{\circ }$ = 1.

$i_c$ = ${\sin }^{-1}$ $\frac{{\mu }_a}{{\mu }_w}$