Question

A ray of light from denser medium strikes a rarer medium at an angle of incidence i. The reflected and refracted rays make an angle of 90${}^{\circ }$ with each other. Angle of reflection and refraction are r & $r^1$. The critical angle is
a) sin ${}^{-1}$ (tan r)
b) sin${}^{-1}$ (cot r)
c) sin ${}^{-1}$(tan $r^1$)
d) sin${}^{-1}$ (cot $r^1$)

• A. only a is correct
• B. only b is correct
• C. a and b are correct
• D. a and d are correct

Answer 1

The correct option is D a and d are correct

$90-\theta +\text{/}90-i=\text{/}90$
$90=\theta +i$
$\mu sini=sin\theta$
$\mu sini=cosi$
$tani=\frac{1}{\mu }$
${\theta }_{lric}=si{n}^{-1}\left(\frac{1}{\mu }\right)=si{n}^{-1}\left(tani\right)$
$=si{n}^{-1}\left(tan{r}^{}\right)$