Akul picks up a large number of sand particles and arranges them in form of a straight line. Mayank meanwhile fetches a source of light like that in lighthouse which throws light only in one direction at a time. This source is rotated with an angular velocity w as shown in the figure. Mayank stands at a distance d from line AB as shown. He starts striking light at A and continues till light strikes all the particles once. As soon as light strikes a particle, It starts moving with a constant speed v in negative y- direction as shown in figure.
In the time Mayank is striking the light, Akul is striking a ray of light as shown in the figure grazing at the glass slab.
Mayank obtains a graph of final shape formed by particles by taking the first particle as origin and taking axes as shown in diagram while Akul obtains a graph of path of light taking origin at point of incidence. They see that the graph obtained by both is same.
Find variation of refractive index n as f(x) if it is known that for any particular x, n does not depend on y.
n=
Give your answer as
Given
w = 5 rad/s
v = 500 cm/s
d = 1m
Details and Assumptions
The sand particles are ideally very small and all the figures formed are to be treated as continuous systems.
Particles don't interfere in each other's way if they don't collide ( There's nothing called friction).
By "grazing" I mean angle of incidence is .
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