Classical Mechanics (Kibble & Berkshire) · Problem 13.8

Hamilton's equations and phase space — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · fermats-principle

Problem

A sugar solution has a refractive index

n

that increases with the depth

z

according to the formula

n = n_0\left(1 + \frac{z}{a}\right)^{1/2},

where

n_0

and

a

are positive constants. A particular ray is horizontal when it passes through the origin of coordinates. Show that the path of the ray is not the straight line

z = 0

but the parabola

z = x^2/4a

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