Someone stop them

Calculus Level 5

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= ( ( i = 1 m a i x i ) + a 0 ) 1 / k ((\sum_{i=1}^m a_{i}*x^{i})+a_{0})^{1/k}

Give your answer as ( i = 1 m a i i ) + a 0 + k (\sum_{i=1}^m a_{i}*i)+a_{0}+k

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 π 2 \frac { \pi }{ 2 } .


Want to have more fun with Mayank and Akul? This question is a part of the set Mayank and Akul


The answer is 12.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

0 solutions

No explanations have been posted yet. Check back later!

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...