# 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.