Question

In the course of a series of duels with your arch nemesis Badok, both he and you (Goodok) are made to stand at the foci of a perfectly reflecting elliptical chamber, with a thick iron obstacle in the center between you. Which point on the wall should you aim your high powered laser gun at the chamber walls so that you are sure to hit Badok? (for simplicity, let both of you exist in a 2-D world)

• A. Point 1 only.
• B. Point 2 only.
• C. Point 3 only.
• D. You can close your eyes and hit any point on the ellipse, and your job will be done.

Answer 1

The correct option is D You can close your eyes and hit any point on the ellipse, and your job will be done.

By the definition of an ellipse, sum of distances of every point of an ellipse from the foci is equal. So, whichever point on the ellipse you hit with your laser gun, the sum of that distance, and the distance from that point to Badok will add up to give the same value! So, all the possible paths are equally short for light! Therefore, as the medium remains the same equivalent distances means same time, so every path is the path of least time! Hence, you can choose any of them. (Remember, of course, light travels in a straight line, as the medium does not change)