When a ray is refracted from one medium to another, the wavelengt… - Vidyadip

MCQ

When a ray is refracted from one medium to another, the wavelength changes from $6000 \,Å$ to $4000\, Å$. The critical angle for the interface will be

A
${\cos ^{ - 1}}\left( {\frac{2}{3}} \right)$
B
${\sin ^{ - 1}}\left( {\frac{2}{{\sqrt 3 }}} \right)$
✓
${\sin ^{ - 1}}\left( {\frac{2}{3}} \right)$
D
${\cos ^{ - 1}}\,\left( {\frac{2}{{\sqrt 3 }}} \right)$

✓

Answer

Correct option: C.

${\sin ^{ - 1}}\left( {\frac{2}{3}} \right)$

c
(c) $_1{\mu _2} = \frac{1}{{\sin C}}$ $ \Rightarrow \frac{{{\mu _2}}}{{{\mu _1}}} = \frac{{{\lambda _1}}}{{{\lambda _2}}} = \frac{1}{{\sin C}}$
$ \Rightarrow \frac{{6000}}{{4000}} = \frac{1}{{\sin C}}$ $ \Rightarrow C = {\sin ^{ - 1}}\left( {\frac{2}{3}} \right)$

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