The Divergent Sibling

A hyperbola has two branches. Rays can reflect as if they came from or head toward the opposite focus, which is why hyperbolic mirrors are useful in telescope optics.

Teaching Notes

Core Idea

Hyperbolas have eccentricity greater than 1 and two disjoint branches.

Try This

Adjust aim offset and track how reflected rays appear to align with the opposite focus.

Teacher Prompt

Discuss why hyperbolic secondary mirrors are used in some telescope designs.

Vocabulary

  • Asymptote: line the curve approaches indefinitely.
  • Branch: one disconnected side of the hyperbola.
  • Eccentricity: for hyperbola, always e > 1.