Question

The $x-z$ plane separates two media $A$ and $B$ of refractive indices $n_{1}=1.5$ and $n_{2}=2.A$ ray of light travels from $A \, $ to $B$ . Its directions in the two media are given by unit vectors $\overset{ \rightarrow }{µ}_{1}=a\hat{i}+b\hat{j}, \, \overset{ \rightarrow }{µ}_{2},=c\hat{i}+d\hat{j},$ then -

• A. $\frac{a}{c}=\frac{4}{3}$
• B. $\frac{a}{c}=\frac{3}{4}$
• C. $\frac{b}{d}=\frac{4}{3}$
• D. $\frac{b}{d}=\frac{3}{4}$

Answer 1

Answer: (A)

$n _{1} \sin i = n _{2} \sin r$
$1.5\left(\vec{\mu}_{1} \times \hat{ j }\right)=2\left(\vec{\mu}_{2} \times \hat{ j }\right)$
$1.5[( a \hat{ i }+ b \hat{ j } \times \hat{ j }]=2[( c \hat{ i }+ d \hat{ j }) \times \hat{ j }]$
$1.5 a \hat{ k }=2 c \hat{ k }$
$\frac{ a }{ c }=\frac{2}{1.5}=\frac{4}{3}$