Question 253: Waves Optics

Question

Two polaroids are placed in the path of unpolarised beam of intensity ' $\mathrm{I}_0$ ' such that no light is emitted from the second polaroid. If a third polaroid whose polarisation axis makes an angle ' $	heta$ ' with the polarisation axis of first polaroid is placed between these polaroids then the intensity of light emerging from the last polaroid will be

Accepted Answer

As no light passes through polaroid 2, polaroid 1 and polaroid 2 are at $90^{\circ}$ to each other.
Polaroid 3 is inserted between then at an angle $	heta$ to polaroid
After polaroid 1 : $\mathrm{I}_1=\frac{\mathrm{I}_0}{2}$
After polaroid 3 : $I_2=I_1 \cos ^2 	heta=\frac{I_0}{2} \cos ^2 	heta$
After polaroid 2 (angle $90^{\circ}-	heta$ to polaroid 3 ) :
$$ \begin{aligned} & I_3=I_2 \sin ^2 	heta=\frac{I_0}{2} \cos ^2 	heta \sin ^2 	heta \ 	herefore & I_3=\frac{I_0}{8}(\sin 2 	heta)^2 \end{aligned} $$

Answer

$\frac{\mathrm{I}_0}{4}(\sin 2 	heta)^2$

Answer

$\frac{\mathrm{I}_0}{8}(\sin 2 	heta)^2$

Answer

$\frac{\mathrm{I}_0}{4} \sin ^2 	heta$

Answer

$\frac{\mathrm{I}_0}{8} \sin ^2 	heta$

Waves Optics

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