Question

A ray of light is incident at an angle i from denser to rare medium. The reflected and the refracted rays are mutually perpendicular. The angle of reflection and the angle of refraction are respectively r and r’, then the critical angle will be

• A. $si{n}^{-1}\left(sinr\right)$
• B. $si{n}^{-1}\left(tan{r}^{\prime }\right)$
• C. $si{n}^{-1}\left(tani\right)$
• D. $ta{n}^{-1}\left(sini\right)$

Answer 1

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

${}_D{\mu }_R=\frac{sini}{sin{r}^{\prime }}{\Rightarrow }_R{\mu }_D=\frac{sin{r}^{\prime }}{sini}=\frac{1}{sinC}\Rightarrow sinC=\frac{sini}{sin(90-r)}=\frac{sini}{cosr}=\frac{sini}{cosi}(as\angle i=\angle r)\Rightarrow sinC=tani\Rightarrow C=si{n}^{-1}\left(tani\right)$