Question

Find the critical angle of the ray of light traveling from glass to water, if refractive indices of glass and water are $5/3$ and $4/3$ respectively.

• A. $i={23}^o{8}^{\prime }$
• B. $i={63}^o{8}^{\prime }$
• C. $i={50}^o{8}^{\prime }$
• D. $i={53}^o{8}^{\prime }$

Answer 1

Answer: (D)

$i={53}^o{8}^{\prime }$

$\text{Critical angle}=c=i$

$\begin{array}{cc}{\mu }_g& =\frac{5}{3}\\ {\mu }_a& =\frac{4}{3}\\ \mu & =\text{refractive index}\\ c& =i=\text{critical angle.}\end{array}$

$\sin c=\frac{1}{{\mu }_g}=g{\mu }_a$

$\sin i=\frac{\frac{4}{3}}{\frac{5}{3}}=\frac{{\mu }_a}{{\mu }_g}$

$\begin{array}{cc}\sin i& =0.8\\ i& ={\sin }^{-1}\left(0.8\right)\\ & ={\sin }^{-1}\left(\frac{4}{5}\right)\\ & ={53}^{\circ }{8}^{\prime }\end{array}$