The law of reflection is quite useful for mirrors and other flat, shiny surfaces. (This sort of reflection is called specular reflection). However, you've likely been told that when you look at something, you are seeing light reflected from the object that you are looking at. This is reflection of a different sort: diffuse reflection. In this problem, you will see how diffuse reflection actually arises from the same law of reflection that you are accustomed to for reflections from mirrors.

Suppose that the spotlight shines so that different parts of the beam reflect off of different two surfaces, one inclined at an angle alpha (from the horizontal) and one inclined at an angle beta. What would the angular separation \Delta \theta be between the rays reflected from the two surfaces? Assume that the light comes at an angle theta_a to the vertical.

Express your answer in terms of some or all of the angles theta_a, alpha, and beta.