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The image of a figure by a reflection is its mirror image in the axis or plane of reflection. For example the mirror image of the small Latin letter p for a reflection with respect to a vertical axis (a vertical reflection) would look like q. Its image by reflection in a horizontal axis (a horizontal reflection) would look like b.
There are several approaches to understanding reflections, but the relationship of reflections to the conservation laws is particularly enlightening. A simple example is a step voltage, () (where is the height of the step and () is the unit step function with time ), applied to one end of a lossless line, and consider what happens when the line is terminated in various ways.
This has the effect of reflecting the plane in the line L, called the reflection axis or the associated mirror. Glide reflections, denoted by G L,d, where L is a line in R 2 and d is a distance. This is a combination of a reflection in the line L and a translation along L by a distance d.
Diagram of Lambertian diffuse reflection. The black arrow shows incident radiance, and the red arrows show the reflected radiant intensity in each direction. When viewed from various angles, the reflected radiant intensity and the apparent area of the surface both vary with the cosine of the viewing angle, so the reflected radiance (intensity per unit area) is the same from all viewing angles.
If one lowers a grid of obstacles into the water, with the spacing between the obstacles roughly corresponding to the wavelength of the water waves, one will see diffraction from the grid. At certain angles between the grid and the oncoming waves, the waves will appear to reflect off the grid; at other angles, the waves will pass through.
A rotation in the plane can be formed by composing a pair of reflections. First reflect a point P to its image P′ on the other side of line L 1. Then reflect P′ to its image P′′ on the other side of line L 2. If lines L 1 and L 2 make an angle θ with one another, then points P and P′′ will make an angle 2θ around point O, the ...
Thus the Cayley graph of the abelian group with the set of generators consisting of four elements (,), (,) is the infinite grid on the plane , while for the direct product with similar generators the Cayley graph is the finite grid on a torus. Cayley graph of the dihedral group on two generators a and b Cayley graph of , on two generators which ...
The number of reflections, or bounces, a "ray" can make, and how it is affected each time it encounters a surface, is controlled by settings in the software. In this image, each ray was allowed to reflect up to 16 times. Multiple "reflections of reflections" can thus be seen in these spheres. (Image created with Cobalt.)