The x-z plane separates two media A and B of refractive indices n1=1.5 and n2=2.A ray of light travels from A to B . Its directions in the two media are given by unit vectors overset arrow µ1=a hati+b hatj, overset arrow µ2,=c hati+d hatj, then -

Question

The x-z plane separates two media A and B of refractive indices n1=1.5 and n2=2.A ray of light travels from A to B . Its directions in the two media are given by unit vectors overset arrow µ1=a hati+b hatj, overset arrow µ2,=c hati+d hatj, then - (A) (a/c)=(4/3) (B) (a/c)=(3/4) (C) (b/d)=(4/3) (D) (b/d)=(3/4)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-jpj2rnpmto5z.png" /> n 1 sin i = n 2 sin r 1.5( vecμ1 × hat j )=2( vecμ2 × hat j ) 1.5[( a hat i + b hat j × hat j ]=2[( c hat i + d hat j ) × hat j ] 1.5 a hat k =2 c hat k ( a / c )=(2/1.5)=(4/3)

Q. 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 $µ \to_{1} = a \hat{i} + b \hat{j}, µ \to_{2}, = c \hat{i} + d \hat{j},$ then -

$\frac{a}{c} = \frac{4}{3}$

$\frac{a}{c} = \frac{3}{4}$

$\frac{b}{d} = \frac{4}{3}$

$\frac{b}{d} = \frac{3}{4}$

$n_{1} sin i = n_{2} sin r$
$1.5 (μ_{1} \times \hat{j}) = 2 (μ_{2} \times \hat{j})$
$1.5 [(a \hat{i} + b \hat{j} \times \hat{j}] = 2 [(c \hat{i} + d \hat{j}) \times \hat{j}]$
$1.5 a \hat{k} = 2 c \hat{k}$
$\frac{a}{c} = \frac{2}{1.5} = \frac{4}{3}$

Q. The x−z plane separates two media A and B of refractive indices n1​=1.5 and n2​=2.A ray of light travels from A to B . Its directions in the two media are given by unit vectors µ→1​=ai^+bj^​,µ→2​,=ci^+dj^​, then -

ca​=34​

ca​=43​

db​=34​

db​=43​