Question

The refractive index of water is $4/3$ and that of glass is $5/3$. What will be the critical angle for the ray of light entering water from the glass?

• A. ${\sin }^{-1}\left(\frac{4}{5}\right)$
• B. ${\sin }^{-1}\left(\frac{5}{4}\right)$
• C. ${\sin }^{-1}\left(\frac{1}{2}\right)$
• D. ${\sin }^{-1}\left(\frac{2}{1}\right)$

Answer 1

Answer: (A)

${\sin }^{-1}\left(\frac{4}{5}\right)$

At critical angle, the ray of light entering water from glass would be refracted at ${90}^{\circ }$.

From Snell's law,

${\mu }_{g}sin{i}_c={\mu }_w$

$⟹sin{i}_c=\frac{{\mu }_w}{{\mu }_g}=\frac{4}{5}$

$⟹i_c=si{n}^{-1}\left(\frac{4}{5}\right)$