Why does every shot sink in the opposite pocket?

In an ellipse, a ray starting from one focus reflects to the other focus. This is the same geometry shown in the elliptical pool-table short: a ball launched from one focus bounces and heads to the pocket at the other focus.

Focus F1 (cue spot) Focus F2 (pocket) Ray path

Tip: drag anywhere on the diagram to swing the laser around focus F1, or use the Laser angle slider.

Try this first

Before you slide anything, point at where you think the yellow ray will go. Then drag the Laser angle slider. Does the ray always reach the other focus?

Semi-major a

Eccentricity e

Laser angle

Burst rays

For projection / teachers

What to look for ↓

Challenge: in pool-table preset mode, can you find any launch angle that misses the pocket at F2?

Teaching Notes

Core Idea

For any point P on an ellipse, the incoming and outgoing ray angles match at the tangent line.

Equivalent claim: a ray from one focus reflects to the other focus.

Try This

Apply the pool-table preset, fire all directions, then vary eccentricity. Ask: what changes and what remains true?

Teacher Prompt

"Can anyone force the reflected ray to miss F2?" Use this to motivate proof from geometry.

Vocabulary

Tangent: line touching curve at one point.
Incident ray: incoming segment before bounce.
Reflected ray: outgoing segment after bounce.