Extra: Reflection of light (not required)

It is well known from physics that if a ray of light hits a mirror, they ray is reflected in such a way that the angle between the mirror and the incoming ray equals the angle between the mirror and the outgoing ray. This fact makes it possible to actually calculate the outgoing ray. Consider the construction below.

Exercise 1

A ray of light passes through the point $A(0\vert -2\vert 1)$ , and hits a mirror. The reflected light passes through point $B(4\vert 3\vert -5)$ . Find the point of reflection $S$ on the mirror, given that the mirror contains the point $P(6 \vert 6\vert 0)$ and has a normal vector $\vec n = \left(\begin{array}{r} 1 \\ 3\\ 2 \end{array}\right)$ .

Solution

Exercise 2

A mirror contains the point $U(0\vert 8\vert 0)$ and has normal vector $\vec{n}=\left(\begin{array}{r} 1 \\ 3\\ 2 \end{array}\right)$ . A ray of light passes through the point $A(0\vert 2\vert 1)$ and hits there mirror where it is reflected. The reflected ray passes through the point $B(4\vert 3\vert -5)$ . Where does the ray of light hit the mirror?

Solution