In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of P₁ and P₂ are orthogonal to each other. The polarizer P₃ covers both the slits with its transmission axis at $45 °$ to those of P₁ and P₂. An unpolarized light of wavelength $λ$ and intensity I0 is incident on P₁ and P₂. The intensity at a point after P3 where the path difference
between the light waves from s₁ and s₂ is $\frac{λ}{3}$ , is

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$I_{0}$

$\frac{I_{0}}{2}$

$\frac{I_{0}}{4}$

$\frac{I_{0}}{3}$

answer is C.

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Detailed Solution

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after passing through third poleriser, Intensity of both the waves must be $\frac{I_{0}}{4}$
now, at a point where path diff is $\frac{λ}{3}$ , phase difference
$\begin{aligned} Δ ϕ = 2 K (\frac{Δx}{λ}) = \frac{2 π}{3} \\ ∴ I_{res} = \sqrt{{(\frac{I_{0}}{4})}^{2} + {(\frac{I_{0}}{4})}^{2} + 2 {(\frac{I_{0}}{4})}^{2}} \cos \frac{2 π}{3} \\ = \frac{I_{0}}{4} \end{aligned}$

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