Search Results for “caustic”
Caustic Formation
Light from C reflects in the tangent to the circle at point B. Observe the trace as B rotates around the circle. While the individual rays move, the phantom curve - the caustic - does not. The caustic is the mathematical envelope of the reflected rays, which is to say that each reflected ray is tangential to the envelope curve. At any moment, each ray is moving with a combination of rotation and translation. Each point on the ray is undergoing a translation. Points on the ray which lie on the caustic are moving along teh length of the ray, and hence their motion is not visible. Which is why the caustic looks stationary while everything else moves.
Caustic curve as focus of parabola
The red curve is f(x) (for -2≤x≤2). The blue curve is the terms up to the square term of the Taylor series. A is the vertex of this parabola, B is its focus. The orange curve is the caustic - envelope of the reflection of vertical rays reflected in a mirror aligned with f(x). Observe that the focus of the parabola traces the caustic.
Caustic of y=f(X)
The thick red curve is y=f(x), initially f(x) = cosh(x). The thinner red curve is the caustic formed by light parallel to the y-axis reflecting in y=f(X). (The caustic is the envelope of the reflected rays. The envelope of a family of lines is the curve which is tangential to the entire family). The blue curve is the parabola which is the 2nd order Taylor expansion of f(X) about the point J I is the focus of this parabola. What do you notice about Ias you drag J?
Parabola Caustic
Rays emanate from D, and their reflections in the parabola form a caustic. See the family of rays by pressing Show, then the caustic curve by pressing Show again. You can drag C and D.
Caustic Cusps
The caustic curve is shown for light emanating from point D. Can you relate the location of the caustic’s cusps to the position of D? Concentric circles are in increments of 0.1 radius
Caustic Clock
The hour hand of this clock defines the radiant point. The minute hand gives the target for a single ray. The second hand gives the target for a family of rays. You can reflect the radiant point in the second hand to observe its relationship to the cusps of the caustic.
Coffee Cup Caustic
Light rays emanate from point C and reflects in the edge of a circle (the coffee cup). The caustic is the phantom curve which appears where the rays concentrate.
Coffee Cup Caustic
You can move the light source and observe the changes in the reflected rays which form the caustic.
Caustic Cusps
Find the direction of the rays which cause the cusps. What do you notice about the reflection angle here?
