How Does Light Expand in a Ring Around a Dusty Star?

[stellaman]

Homework Statement

A star surrounded by a sphere of dust with a radius R. The star emits a short bright flash of light, it is absorbed and re-emitted by the dust. Someone much further away than R sees the light, first at a point on the shell and then in an expanding ring.

A)Show that the rate dr/dt of the ring expanding is given in an appropriate first order approximation by: dr/dt=(speed of light)(cot(theta))

The Attempt at a Solution

I have really know idea how to start this one. I could really use a hint to get started.

 

[tiny-tim]

Welcome to PF!

Hi stellaman! Welcome to PF!

Essentially, this is a sphere which lights up all at the same time.

You have to calculate the time t(θ) when the light from angle θ arrives on Earth.

Then convert θ to the "sideways" distance x from the axis, and get dx/dt.