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BITSAT 2024
Exam
BITSAT
Year
2024
Subject
Physics
Chapter
Wave Optics

BITSAT 2024 · Physics · Wave Optics

Young's double slit experiment is performed in a medium of...

Young's double slit experiment is performed in a medium of refractive index of 1.33. The maximum intensity is I0I_0. The intensity at a point on the screen, where path difference between the light coming out from slits is λ4\frac{\lambda}{4}, is

Options

  1. A0
  2. BI02\frac{I_0}{2}
  3. C3I08\frac{3 I_0}{8}
  4. D2I03\frac{2 I_0}{3}

Correct answer

B. I02\frac{I_0}{2}

Step-by-step solution

Given, path difference, Δx=λ4\Delta x=\frac{\lambda}{4} Phase difference, ϕ=(2πλ)×\phi=\left(\frac{2 \pi}{\lambda}\right) \times (Path difference) =2πλ×λ4=π2...(i)=\frac{2 \pi}{\lambda} \times \frac{\lambda}{4}=\frac{\pi}{2}...(i) It is given that, maximum intensity is I0I_0. So, intensity at a point on the screen, where phase difference ϕ\phi is given by I=I0cos⁡2(ϕ2)=I0×cos⁡2(π/22)[∵ using Eq.(i) ]=I0×(12)2=I02\begin{aligned} I & =I_0 \cos ^2\left(\frac{\phi}{2}\right) \\ & =I_0 \times \cos ^2\left(\frac{\pi / 2}{2}\right) \quad[\because \text{ using Eq.(i) }] \\ & =I_0 \times\left(\frac{1}{\sqrt{2}}\right)^2 \\ & =\frac{I_0}{2} \end{aligned}
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