First slide

Polarisation

Question

Unpolarised light of intensity $32 {Wm}^{- 2}$ passes through three polarizers such that transmission axes of the first and second polarizer makes and angle 30⁰ 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

Moderate

A

$32 {Wm}^{- 2}$
B

$3 {Wm}^{- 2}$
C

$8 {Wm}^{- 2}$
D

$4 {Wm}^{- 2}$

Solution

Angle between $P_{1} and P_{2} = 30^{\circ} (given)$
Angle between $P_{2} and P_{3} = θ = 90^{\circ} - 30^{\circ} = 60^{\circ}$
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
$I_{2} = I_{1} \cos^{2} 30^{\circ} = 16 {(\frac{\sqrt{3}}{2})}^{2} = 12 \frac{W}{m^{2}}$
Similarly intensity of light transmitted by P₃ is
$I_{3} = I_{2} \cos^{2} θ = 12 \cos^{2} 60^{\circ} = 12 {(\frac{1}{2})}^{2} = 3 \frac{W}{m^{2}}$

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