Two media A and B of refractive indices  ${\mu }_1=1.5\text{ and }{\mu }_2=2$ are separated by  $x-z$ plane. A ray of light travels from A to B. The incident ray and the reflected ray are represented by unit vectors ${\overrightarrow{u}}_1=a\widehat{i}+b\widehat{j}\text{ and }{\overrightarrow{u}}_2=c\widehat{i}+d\widehat{j}.$  Then 

Applying Snell’s Law at the interface separating two media, we get  ${\mu }_1\sin i={\mu }_2\sin r$

From the figure, we get
 $\left(\frac{3}{2}\right)\left(\frac{a}{\sqrt{a^2+b^2}}\right)=2\left(\frac{c}{\sqrt{c^2+d^2}}\right)$
Since  $a\widehat{i}+b\widehat{j}\text{ and }c\widehat{i}+d\widehat{j}$ are unit vectors, so we get  $\sqrt{a^2+b^2}=\sqrt{c^2+d^2}=1$
 Substituting in equation, we get  $\frac{a}{c}=\frac{4}{3}$