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 differencebetween the light waves from s1 and s2 isλ3, is

after passing through third poleriser, Intensity of both the waves must be I04now, at a point where path diff is λ3, phase difference Δϕ=2K(Δxλ)=2π3 ∴Ires=(I04)2+(I04)2+2(I04)2cos⁡2π3 =I04

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 differencebetween the light waves from s1 and s2 isλ3, is

after passing through third poleriser, Intensity of both the waves must be I04now, at a point where path diff is λ3, phase difference Δϕ=2K(Δxλ)=2π3 ∴Ires=(I04)2+(I04)2+2(I04)2cos⁡2π3 =I04

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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
$\begin{aligned} Δ ϕ = 2 K (\frac{Δx}{λ}) = \frac{2 π}{3} \\ ∴ I_{res} = \sqrt{{(\frac{I_{0}}{4})}^{2} + {(\frac{I_{0}}{4})}^{2} + 2 {(\frac{I_{0}}{4})}^{2}} \cos \frac{2 π}{3} \\ = \frac{I_{0}}{4} \end{aligned}$