![]() ![]() This derivation makes use of the calculus of maximum-minimum determination and the definitions of the triangle trig functions. a b 90 Supplementary angles (sum to 180°) a d 180 Vertically opposite angles (equal) a c Angles in a revolution sum to 360°. Materials: One mirror One power supply One light box kit One protractor One A4 sheet of paper. ![]() We make use of the index of refraction, defined as n=c/v. The angle of reflection will equal the angle of incidence. Snell's Law can be derived from this by setting the derivative of the time =0. Fermat's Principle for Refractionįermat's Principle: Light follows the path of least time. This derivation makes use of the calculus of maximum-minimum determination, the derivative of a square root, and the definitions of the triangle trig functions. What are the angles of incidence equal to the angle of reflection This is called the law of reflection. This may be found by setting the derivative of L with respect to x equal to zero. Since the speed is constant, theminimum time path is simply the minimum distance path. The law of reflection can be derived from this principle as follows: Of course the straight line from A to B is the shortest time, but suppose it has a single reflection. The law of reflection gives the familiar reflected image in a planemirror where the image distancebehind the mirror is the same as the object distance in front of themirror.įermat's Principle: Light follows the path of least time. This law of reflection can be derived from Fermat's principle. Both angles are typically measured with respect to the normal to the surface. Sanders, Nonlinearity 22 1499–1522 (2009).Reflection and Fermat's Principle Law of ReflectionĪ light ray incident upon a reflective surface will be reflected at an angle equal to the incident angle. There are references to earlier studies of this model, of which the earliest isīifurcations of periodic and chaotic attractors in pinball billiards An important question is whether the polygon has parallel sides, which tend to stabilise the dynamics, as your simulations have found. The law of reflection is quite simple, as it states that the angle of reflection is equal to the angle of incidence. Section 5 deals with generic polygons, 6 with regular polygons, 7 with acute triangles and 8 with rectangles. 329 687-723 (2014).Īs the title indicates, the emphasis is on chaotic dynamics (in contrast to polygonal billiards with the usual reflection law, for which the entropy is always zero). In the law of reflection, students do not often question why the angle of incidence is equal to the angle of reflection and why a light ray should follow this specific path. The initial topics that are introduced through their lessons are laws of reflection and refraction of light. SRB measures for polygonal billiards with contracting reflection laws G. Students are often introduced to optics in their middle school years. This kind of billiard has been studied recently, under the name "Pinball billiards" (though this term has been used in other contexts, too) or more generally "Contracting reflection laws." The most recent appears to be If so, I would appreciate pointers-Thanks! Perhaps these questions have been explored. "billiard table" is a nonsquare rectangle, or other some convex shape. We describe the path of light as straight-line rays Reflection off a flat surface follows a simple rule: angle in (incidence) equals angle out (reflection). ![]() (2) what might be the dynamics when reflectionĪngles are some other fraction of the incident angles, and (3) when the I explored this a bit with the angle of reflection $\frac$-reflection paths illustrated above, Of the angle of incidence, rather than equal to it. The Angle of Incidence Formula We can find the angle of incidence by using Snells Law. In a mirrored square) has the property that the angle of reflection is a fraction The angle of incidence is ALWAYS equal to the angle of reflection This is one of the laws of reflection. Which of the Labelled angles is equal to angle of reflection angle of incidence 1. According to the law of reflection, the angle of incidence equals the angle of reflection. Suppose that a billiard ball bouncing in a unit square (or a lightray reflecting 6A10.11 ANGLE OF INCIDENCE AND REFLECTION A beam of light reflecting off a mirror attached to an angle scale proves that the angle of incidence equals the angle of reflection. The angle of incidence is the angle between this normal and the incident ray the angle of reflection is the angle between this normal and the reflected ray. ![]()
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