Reflecting inside a Spherical Mirror and a Catacaustic

​
object arrow tip
a
-0.5
h
0.4
radius
r
0.8
show catacaustic
show images of A
show a ray from C
This Demonstration shows an image formed inside a spherical mirror of radius
r
and center
S
on the optical axis
α
. Let the point
A
be off
α
and let
C
be the orthogonal projection of
A
onto
α
. After reflection, the reflection of the ray parallel to
α
from
A
meets the ray
AS
at the point
B
. The notion of image of a point is not uniquely defined because the reflections of three rays from a given point do not meet in a single point. The image of the directed segment
CA
is a vertical segment with endpoint
B
as
r∞
. If you increase the height
h
of
A
,
B
moves to the right.
The catacaustic is also shown.

External Links

Catacaustic (Wolfram MathWorld)
Circle Catacaustic (Wolfram MathWorld)
Spherical Mirror (Wolfram MathWorld)
Mirror Image (Wolfram MathWorld)
Catacaustics for Some Graphs
Ray Diagrams for Spherical Mirrors
Tracing Rays Reflected from a Spherical Mirror

Permanent Citation

Izidor Hafner
​
​"Reflecting inside a Spherical Mirror and a Catacaustic"​
​http://demonstrations.wolfram.com/ReflectingInsideASphericalMirrorAndACatacaustic/​
​Wolfram Demonstrations Project​
​Published: October 1, 2018