Parabola: Reflective Property
- Brian Sterr
In the diagram below, you can move to be any point on the parabola.
- First, consider a ray that is parallel to the axis of symmetry of the parabola and coming in to point . [Show the ray] How will it be reflected off of the surface of the parabola? We can find the angles of incidence and reflection by using the tangent line to the parabola at . [Show the tangent]
- Now we can also look at the two segments and . By the definition of a parabola they are congruent. Also, notice that . [Show segments from ]
- Consider where is the y-intercept of the tangent line. Notice that
- So we have
- This means . Why?
- Also we can conclude that . Why?
- In conclusion, because , we know that the ray to will be reflected along to . [Show the arrows]
- You can drag around to see that this will always be true at any point on the parabola.