Conic sections – the reflective property (satellite dish, whispering gallery, telescope)

What it shows

Each conic section has a reflective property tied to its foci, which follows from the law of reflection: the reflected ray makes the same angle with the normal as the incoming ray. Rays parallel to the axis of a parabola all reflect through the focus, so a receiver placed there collects the whole signal. In an ellipse, a ray from one focus reflects through the other, and because MF₁ + MF₂ = 2a every path has the same length, so the waves arrive together. For a hyperbola, a ray aimed at one focus reflects towards the other, which is how the secondary mirror of a Cassegrain telescope works.

How to use

Choose the Conic, set Number of rays and follow the orange ray with its purple normal. Move the Dish depth or Eccentricity slider to show that the property holds for every shape, not just one. Then move the offset slider (Dish misalignment, Source offset from F₁ or Aim offset) and read the average miss distance: the reflected rays no longer meet at the focus, which explains why real dishes, lithotripters and telescopes need careful alignment.

Parameters you can change

• Conic Parabola – satellite dish, Ellipse – lithotripter, Hyperbola – Cassegrain telescope
• Shape (p for parabola / eccentricity e) 0.2–0.95
• Number of rays 3–21

Questions to explore

1. If a lamp is placed at the focus of a parabolic mirror, what does the reflected beam look like?
2. Why does a lithotripter put the shock-wave source at one focus of an ellipse and the kidney stone at the other?
3. When the eccentricity changes, do the reflected rays still pass through the focus? What does that tell you?