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 $ vs $sin\,r $ 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$ ${i_c} = \frac{1}{{\sqrt 3 }}$
✓
Both ($b$) and ($c$)

✓

Answer

Correct option: D.

Both ($b$) and ($c$)

d
$(b,c)$ From graph $\tan {30^o} = \frac{{\sin r}}{{\sin i}} = \frac{1}{{_1{\mu _2}}}$

==> $_1{\mu _2} = \sqrt 3 $ ==> $\frac{{{\mu _2}}}{{{\mu _1}}} = \frac{{{v_1}}}{{{v_2}}} = 1.73$ ==>${v_1} = 1.73\,{v_2}$

Also from $\mu = \frac{1}{{\sin C}}$ ==> $\sin C = \frac{1}{{_{Rarer}{\mu _{Denser}}}}$

==> $\sin C = \frac{1}{{_1{\mu _2}}} = \frac{1}{{\sqrt 3 }}$.

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