![]() ![]() It is virtual, meaning that the image appears to be behind the mirror, and cannot be projected onto a screen.It is the same distance behind the mirror as the object is in front.The image in a flat mirror has these features: See also: Mirror image § In three dimensions ![]() Given an incident direction d ^ i Reflected images The direction of a reflected ray is determined by the vector of incidence and the surface normal vector. The law of reflection can also be equivalently expressed using linear algebra. When the boundary size is much larger than the wavelength, then the electromagnetic fields at the boundary are oscillating exactly in phase only for the specular direction. The phenomenon of reflection arises from the diffraction of a plane wave on a flat boundary. When the light impinges perpendicularly to the surface, it is reflected straight back in the source direction. The law of reflection states that the angle of reflection of a ray equals the angle of incidence, and that the incident direction, the surface normal, and the reflected direction are coplanar. Reflection of the incident ray also occurs in the plane of incidence. When a ray encounters a surface, the angle that the wave normal makes with respect to the surface normal is called the angle of incidence and the plane defined by both directions is the plane of incidence. A ray of light is characterized by the direction normal to the wave front ( wave normal). Light propagates in space as a wave front of electromagnetic fields. The reflecting material of mirrors is usually aluminum or silver. A surface built from a non-absorbing powder, such as plaster, can be a nearly perfect diffuser, whereas polished metallic objects can specularly reflect light very efficiently. Matte paints exhibit essentially complete diffuse reflection, while glossy paints show a larger component of specular behavior. The distinction may be illustrated with surfaces coated with glossy paint and matte paint. Specular reflection reflects all light which arrives from a given direction at the same angle, whereas diffuse reflection reflects light in a broad range of directions. Reflection may occur as specular, or mirror-like, reflection and diffuse reflection. The Fresnel equations describe the physics at the optical boundary. In general, reflection increases with increasing angle of incidence, and with increasing absorptivity at the boundary. The degree of participation of each of these processes in the transmission is a function of the frequency, or wavelength, of the light, its polarization, and its angle of incidence. Optical processes, which comprise reflection and refraction, are expressed by the difference of the refractive index on both sides of the boundary, whereas reflectance and absorption are the real and imaginary parts of the response due to the electronic structure of the material. So the image (that is, point B) is the point (1/25, 232/25).When light encounters a boundary of a material, it is affected by the optical and electronic response functions of the material to electromagnetic waves. So the intersection of the two lines is the point C(51/50, 457/50). Now we need to find the intersection of the lines y = 7x + 2 and y = (-1/7)x + 65/7 by solving this system of equations. So the equation of this line is y = (-1/7)x + 65/7. So the desired line has an equation of the form y = (-1/7)x + b. Since the line y = 7x + 2 has slope 7, the desired line (that is, line AB) has slope -1/7 as well as passing through (2,9). So we first find the equation of the line through (2,9) that is perpendicular to the line y = 7x + 2. Then, using the fact that C is the midpoint of segment AB, we can finally determine point B.Įxample: suppose we want to reflect the point A(2,9) about the line k with equation y = 7x + 2. Then we can algebraically find point C, which is the intersection of these two lines. So we can first find the equation of the line through point A that is perpendicular to line k. Note that line AB must be perpendicular to line k, and C must be the midpoint of segment AB (from the definition of a reflection). Let A be the point to be reflected, let k be the line about which the point is reflected, let B represent the desired point (image), and let C represent the intersection of line k and line AB. ![]()
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