Question

A ray of light from denser medium strikes a rarer medium at angle of incidence $i$. The reflected and refracted rays make an angle of ${90}^o$ with each other. The angle of reflection and refraction are $r$ and $r^{\prime }$. The critical angle is

• A. $si{n}^{-1}\left(tanr\right)$
• B. $si{n}^{-1}\left(tani\right)$
• C. $si{n}^{-1}\left(tan{r}^{\prime }\right)$
• D. $si{n}^{-1}\left(tan\right(i+r\left)\right)$

Answer 1

The correct option is B $si{n}^{-1}\left(tani\right)$

Since incident ray is in denser medium we have,
$\frac{1}{\mu }=\frac{sini}{sin{r}^{\prime }}$

But $r^{\prime }={90}^{\circ }-r$ and $i=r$

So, $\frac{1}{\mu }=\frac{sini}{sin({90}^{\circ }-r)}=\frac{sini}{cosr}=\frac{sini}{cosi}=tani$

Again if $C=$ Critical angle, then $\mu =\frac{1}{sinC}$

or
$SinC=\frac{1}{\mu }$

$C=si{n}^{-1}\left(\frac{1}{\mu }\right)$

$=si{n}^{-1}\left(tani\right)$