Answer:
According to Brewster law, when a ray of light is incident on a transparent refracting medium at polarising angle, \[\mu =\tan {{i}_{p}}\] But \[{{I}_{p}}+{{r}_{p}}={{90}^{\circ }}\] or \[{{i}_{p}}={{90}^{\circ }}-{{r}_{p}}\] \[\therefore \] \[\mu =\tan ({{90}^{\circ }}-{{r}_{p}})=\cot {{r}_{p}}=\frac{1}{\tan {{r}_{p}}}\]?.(i) As \[{{i}_{c}}\]is the critical angle for the transparent medium, so \[\mu =\frac{1}{\sin {{i}_{c}}}\] ? (ii) On comparing (i) and (ii) , we get \[\tan {{r}_{p}}=\sin {{i}_{c}}\] or \[{{r}_{p}}={{\tan }^{-1}}(\sin {{i}_{c}})\].
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