# Someone stop them

**Calculus**Level 5

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

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

**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 \(\frac { \pi }{ 2 } \).