In a YDSE experiment, one of the slits is covered with a glass plate of thickness (2.4×10−4) meter, refractive index of which varies with time as μ=t2+12t+8. The separation between the slits is 2×10−3 meter and the distance between the plane of slits and the screen is 2 meters.  Find the velocity (in m/s) of the central maxima at t = 4 s.  (Take refractive index of air = 1).(Round off to nearest integer)

# In a YDSE experiment, one of the slits is covered with a glass plate of thickness $\left(2.4×{10}^{-4}\right)$ meter, refractive index of which varies with time as $\mu ={t}^{2}+12t+8.$ The separation between the slits is $2×{10}^{-3}$ meter and the distance between the plane of slits and the screen is 2 meters.  Find the velocity (in m/s) of the central maxima at t = 4 s.  (Take refractive index of air = 1).(Round off to nearest integer)

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### Solution:

$\left(\mu -1\right){t}_{0}=\frac{d×y}{D}$

$v=\frac{dy}{dt}=\left(2t+12\right)×\frac{2.4×{10}^{-4}×2}{2×{10}^{-3}}$

$v=4.8\text{\hspace{0.17em}}m/s$

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