question_answer

Two polaroids \[{{P}_{1}}\] and \[{{P}_{2}}\] are placed with their pass axes perpendicular to each other. Unpolarised light of intensity \[{{I}_{0}}\] is incident on \[{{P}_{1}}.\]  A third polaroid \[{{P}_{3}}\] is kept in between \[{{P}_{2}}\] such that its pass axis makes an angle of \[30{}^\circ \] with that of \[{{P}_{1}}.\] Determine the intensity of light transmitted through \[{{P}_{3}}.\]

Answer:

According to the question, Intensity through \[{{P}_{1}},{{I}_{1}}=\frac{{{I}_{0}}}{2}\] Intensity through \[{{P}_{3}},\] \[{{I}_{3}}={{I}_{1}}{{\cos }^{2}}30{}^\circ \] (from malus? law, \[I={{I}_{0}}{{\cos }^{2}}\theta \]) \[=\frac{{{I}_{0}}}{2}{{\left( \frac{\sqrt{3}}{2} \right)}^{2}}\]             \[\left( \because \cos 30{}^\circ =\frac{\sqrt{3}}{2} \right)\] Therefore, intensity through \[{{P}_{2}},\] \[{{I}_{2}}={{I}_{3}}{{\cos }^{2}}60{}^\circ \]             \[=\frac{{{I}_{0}}}{2}.\frac{3}{4}.{{\left( \frac{1}{2} \right)}^{2}}\]    \[(\because v\cos \,60{}^\circ =1/2)\]             \[=\frac{3}{32}{{I}_{0}}\]