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 angle $r$, the graph of $\sin i v s \sin r$ is as shown in the graph. From this, one can conclude that

A
(a) Velocity of light in the second medium is 1.73 times the velocity of light in the 1 medium
B
(b) Velocity of light in the 1 medium is 1.73 times the velocity in the 11 medium
C
The critical angle for the two media is given by
$
\sin i_c=\frac{1}{\sqrt{3}}
$
(c) The critical angle for the two media is given by
$
\sin i_c=\frac{1}{\sqrt{3}}
$
D
(d) $\sin i_c=\frac{1}{2}$

✓

Answer

(b, c) From graph $\tan 30^{\circ}=\frac{\sin r}{\sin i}=\frac{1}{{ }_1 \mu_2}$$\Rightarrow{ }_1 \mu_2=\sqrt{3} \Rightarrow \frac{\mu_2}{\mu_1}=\frac{v_1}{v_2}=1.73\Rightarrow v_1=1.73 v_2$Also from $\mu=\frac{1}{\sin C} \Rightarrow \sin C=\frac{1}{\text { Rarer } \mu_{\text {Denser }}}$$\Rightarrow \sin C=\frac{1}{{ }_1 \mu_2}=\frac{1}{\sqrt{3}}$

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