![]() ![]() The angle of incidence of ray is measured from the normal to the plane it intersects and congruent angles have congruent angles have congruent complements, so it follows that the angles of incidence are congruent. Angle AMO and NMB' are vertical angles and vertical angles are congruent. It can be proven triangles MNB and MNB' are congruent by the SAS rule of congruent triangles. The angle of incidence and the angle of reflection are calculated by drawing a normal line that is perpendicular to the reflecting surface. These values for the angle of incidence and refraction are consistent with Snell's Law. The angle of refraction in the air is approximately 57. At this angle, the light refracts out of the water into the surrounding air bending away from the normal. Let P be a point also on the mirror on the opposite of M from N but the same distance. The angle of incidence in the water is approximately 39. Now consider a line dropped from B to B' and call where it intersects the mirror N. This line also intersects the mirror at M. The argument is reversible starting from B and traveling to a reflected point of A, call it A'. So the line from A to B' intersects the mirror at a point M that minimizes A to M to B travel distance/time. The shortest distance between two points is a straight line and by the Pythagorean Theorem it can be shown that the distance form M to B and the distance from M to B' are the same for any point M. The law of reflection states that when a ray of light is reflected off a surface, the angle of incidence is equal to the angle of reflection. Angle between the reflected ray and the normal is called angle of reflection. One could also consider the problem if a point B' is added as a reflection of the point B. Angle between the incident ray and the normal is called angle of incidence. One can use the Pythagorean theorem and calculus to solve this. Find a point M on the mirror between these two such that the sum of the distance from A to M and from M to B is minimized. Suppose you have two points A and B above a mirror at different heights above the mirror. These will serve to guide a geometric argument for equal angles. If the speed of light remains constant in the material, the principle of Least Time becomes a principle of least distance. In the case of physical principles, some of these will be just reliable observations.įermat's Least Time Principle tells us that light take the least time path between possible trajectories. For example, if a light ray hits a surface with an angle of incidence of 45°, it will be reflected with an angle. A proof requires axioms, basic statements that can't be proven. The law of reflection states that: angle of incidence i angle of reflection r. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |