First slide

Diffraction of light-Wave Optics

Question

Two polaroids are placed in the path of unpolarized beam of intensity I₀ such that no light is emitted from the second polaroid. If a third polaroid whose polarization axis makes an angle $θ$ with the polarization axis of first polaroid, is placed between these polaroids then the intensity of light emerging from the last polaroid will be

Moderate

A

$(\frac{I_{0}}{8}) \sin^{2} 2 θ$
B

$(\frac{I_{0}}{4}) \sin^{2} 2 θ$
C

$(\frac{I_{0}}{24}) \cos^{4} 2 θ$
D

$I_{0} \cos^{4} θ$

Solution

No light is emitted from the second polaroid, so P₁ and P₂ are perpendicular to each other
Let the initial intensity of light is I₀. So intensity of light after transmission from first polaroid = $\frac{I_{0}}{2}$ .
Intensity of light emitted from $P_{3} = I_{1} = \frac{I_{0}}{2} \cos^{2} θ$
Intensity of light transmitted from last polaroid i.e. from $P_{2} = I_{1} \cos^{2} (90^{0} - θ) = \frac{I_{0}}{2} \cos^{2} θ . \sin^{2} θ$ $= \frac{I_{0}}{2 \times 4} {(4 \sin^{2} θ \cos^{2} θ)}^{} = \frac{I_{0}}{8} {(2 \sin θ \cos θ)}^{2} = \frac{I_{0}}{8} \sin^{2} 2 θ (∵ θ_{1} + θ_{2} = 90, \sin 2 θ = 2 \sin θ \cos θ)$

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