question_answer

Values for Brewster's angle can be

A)  only less than \[{{45}^{o}}\]

B)  only greater than \[{{45}^{o}}\]

C)  any value in the range \[{{0}^{o}}\] to \[{{90}^{o}}\] except \[{{45}^{o}}\]

D)  any value in the range \[{{0}^{o}}\] to \[{{90}^{o}}\] including \[{{45}^{o}}\]

Correct Answer: C

Solution :

Brewster's angle corresponding to two media of refractive indices \[{{r}_{1}}\] and \[{{r}_{2}}\] is    \[\tan \,\,{{i}_{B}}=\left( \frac{{{n}_{2}}}{{{n}_{1}}} \right)\] Where, \[{{n}_{2}}\] is refractive index of denser medium and \[{{n}_{1}}\] is refractive index of rarer medium. If two mediums are same, i.e. \[{{n}_{1}}={{n}_{2}}\Rightarrow \tan \,\,{{i}_{B}}=1\] or \[{{i}_{B}}={{45}^{o}}\] Polarisation is not possible if two mediums are same. Therefore \[{{i}_{B}}\ne {{45}^{o}}\] Hence, Brewster's angle can have any value in the range \[{{0}^{o}}\] to \[{{90}^{o}}\] except \[{{45}^{o}}\].