A Parabolic Mirror

focal parameter p

10

number of rays n

3

2

y

= 20 x

Given a point F (the focus) and a line

d

(the directrix) that lie in a plane, the locus of points in that plane that are equidistant from F and

d

is a parabola.

One form of the equation of a parabola is

2

y

=2px

, where the focal parameter

p

is the distance from F to

d

.

This Demonstration illustrates the reflection property of parabolas. Imagine that the parabola is a mirror and that there is a light source at the focus. Then all the reflected rays are parallel to the axis of symmetry of the parabola.