When light is incident on a medium at angle i and refracted into … - Vidyadip

MCQ

When light is incident on a medium at angle $i$ and refracted into a second medium at an angale $r,$ the graph of $\sin i$ vs $\sin r$ is as shown in the graph. From this, one can conclude that is as shown in the graph. From this, one can conclude that :-

$(a)$ Velocity of light in the second medium is $1.73$ times the velocity of light in the $I$ medium

$(b)$ Velocity of light in the $I$ medium is $1.73$ times the velocity in the $II$ medium

$(c)$ The critical angle for the two media is given by $\sin \,{i_c}\, = \,\frac{1}{{\sqrt 3 }}$

$(d)$ $\sin \,{i_c}\, = \,\frac{1}{2}$

A
$a,c$
✓
$b,c$
C
$a,d$
D
$b,d$

✓

Answer

Correct option: B.

$b,c$

b
${\,_1}{\mu _2} = \frac{{\sin {\rm{i}}}}{{\sin {\rm{r}}}} = \frac{{{\mu _2}}}{{{\mu _1}}} = \frac{{{{\rm{v}}_1}}}{{{{\rm{v}}_2}}} = \frac{1}{{\tan {{30}^\circ }}} = \sqrt 3 = 1.732$

$\mathrm{i}_{\mathrm{c}}=\sin ^{-1} \frac{\mu_{1}}{\mu_{2}}=\sin ^{-1} \frac{1}{\sqrt{3}}$

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