1
$\begingroup$

The problem is as follows: point A , plane x and lines m and n are given in 3d Space. Ray of light passes through m and n and is reflected via the plane x, then the reflected ray passes through the point A, find the ray and the reflected ray

Problem in GeoGebra : enter image description here

Can someone explain the method of solving these kind of problems. Thanks in advance

$\endgroup$
0
$\begingroup$

There are a few ways to approach this, but they all hinge on two key properties of reflection. First is Snell’s law of reflection: the angle of incidence is equal to the angle of reflection. The second is that a ray through $\mathbf A$ and its reflection from $\mathbf x$ lie in a plane through $\mathbf A$ that is perpendicular to $\mathbf x$. Using these properties, one can attack the problem in a few slightly different ways.

There’s also a trick that you can use to simplify many of these reflection problems: if you extend the incident ray whose reflection passes through $\mathbf A$ beyond the mirror surface, it will pass through the reflection (used in a different sense) of $\mathbf A$ on the other side of the mirror plane $\mathbf x$. This trick is an application of the above properties.

So, for this particular problem, I would proceed by finding the reflection $\mathbf A'$ of $\mathbf A$ in the plane $\mathbf x$, and then finding a perpendicular plane through $\mathbf A'$ such that its intersections with the two lines and $\mathbf A'$ are colinear. From there, computing the two rays and the point of reflection is a straightforward computation.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.