question_answer

Unpolarized light of intensity 32Wm?2 passes through three polarizers such that transmission axes of the first and second polarizer makes and angle 30° with each other and the transmission axis of the last polarizer is crossed with that of the first. The intensity of final emerging light will be

A)            32 Wm?2                                 

B)            3 Wm?2

C)            8 Wm?2                                   

D)            4 Wm?2

Correct Answer: B

Solution :

                   Angle between P1 and P2 = 30° (given) Angle between P2 and P3 = q = 90° ? 30° = 60° The intensity of light transmitted by P1 is \[{{I}_{1}}=\frac{{{I}_{0}}}{2}=\frac{32}{2}=16\frac{W}{{{m}^{2}}}\] According to Malus law the intensity of light transmitted by P2 is \[{{I}_{2}}={{I}_{1}}{{\cos }^{2}}30{}^\circ =16\,{{\left( \frac{\sqrt{3}}{2} \right)}^{2}}=12\,\frac{W}{{{m}^{2}}}\] Similarly intensity of light transmitted by P3 is \[{{I}_{3}}={{I}_{2}}{{\cos }^{2}}\theta =12{{\cos }^{2}}60{}^\circ =12\,{{\left( \frac{1}{2} \right)}^{2}}=3\frac{W}{{{m}^{2}}}\]