Challenges in optics 4

Young's double slit experiment is performed. The distance between two slits is dd. The distance between slit plane and screen is DD. Now, there exists a liquid of refractive index r0r_{0}. The refractive index of the liquid is raised with time as per the law: r=r0+at+bt2r=r_{0}+at+bt^{2}, where aa and bb are constants. Find the velocity of the central maxima at time t=5 st=5\text{ s}.

Enter the answer upto 5 decimal places.

Details and Assumptions

  • a=2 s1a=2 \text{ s}^{-1}, b=4 s2b=4\text{ s}^{-2}, θ=30\theta=30^{\circ}, D=1 mD=1\text{ m}, r0=6r_{0}=6, DdD \gg d.

  • All measurements are in SI units.

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