A ray of light travels from a medium of refractive index µ to air its angle of incidence in the medium is i measured from the normal to the boundary and its angle of deviation is δ. If δ is plotted against i , which of the following best represents the resulting curve?

The ray of light is refracted at the plane surface. However, since the ray is travelling from a denser to a rarer medium, for an angle of incidence (i) greater then the critical angle (c) the ray will be totally internally reflected.

$\begin{array}{l}\mathrm{For}\mathrm{i}<\mathrm{c};\mathrm{deviation}\mathrm{\delta }=\mathrm{r}-\mathrm{i} \mathrm{with}\frac{1}{\mathrm{\mu }}=\frac{\sin \mathrm{i}}{\sin \mathrm{r}}\\ \mathrm{Hence}\mathrm{\delta }={\sin }^{-1}\left(\mathrm{\mu }-\sin \mathrm{i}\right)-\mathrm{i}\\ \mathrm{This}\mathrm{is}\mathrm{a}\mathrm{non}-\mathrm{linear}\mathrm{relation}.\mathrm{The}\mathrm{maximum}\mathrm{value}\mathrm{of}\mathrm{\delta }\mathrm{is}\\ {\mathrm{\delta }}_1=\frac{\mathrm{\pi }}{2}-\mathrm{c};\mathrm{where}\mathrm{i}=\mathrm{c}\mathrm{and}\mathrm{\mu }=\frac{1}{\sin \mathrm{c}}\end{array}$

$\begin{array}{l}\mathrm{For}\mathrm{i}>\mathrm{c},\mathrm{deviation}\mathrm{d}=\mathrm{\pi }-2\mathrm{i}\\ \mathrm{\delta }\mathrm{decreases}\mathrm{linearly}\mathrm{with}\mathrm{i}.\\ {\mathrm{\delta }}_2=\mathrm{\pi }-2\mathrm{c}=2{\mathrm{\delta }}_1\end{array}$