# Challenges in optics 4

Classical Mechanics Level 5

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

Enter the answer upto 5 decimal places.

Details and Assumptions

• $$a=2 \text{ s}^{-1}$$, $$b=4\text{ s}^{-2}$$, $$\theta=30^{\circ}$$, $$D=1\text{ m}$$, $$r_{0}=6$$, $$D \gg d$$.

• All measurements are in SI units.

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