# . Explain the Concept of two Mirrors placed at an Angle to Each Other

If two plane mirrors are placed together on one of their edges so as to form a right angle mirror system and then the angle between them is decreased, some interesting observations can be made. One observes that as the angle between the mirrors decreases, the number of images that can be seen increases. In fact as the angle between the mirrors approaches 0 degrees (i.e., the mirrors are parallel to each other), the number of images approaches infinity.

The generation of two images is not difficult to explain; each of the two mirrors produces an image due to the single reflection of light off one of the mirror faces to an observer's eye. The remaining images are produced as the result of multiple reflections of light off more than one of the faces. Right angle mirrors will allow a maximum of two reflections of light from the object. But as the angle decreases, three, four, and even more reflections can occur.

Determining the image locations for such multiple mirror systems can become complicated. First determine the location of the primary images using the principle that the image distance to the mirror is the same as the object distance to the mirror. Each primary image forms a secondary image as a result of a double reflection. By extending one of the mirror lines, a primary image can be reflected across the second mirror line to form a secondary image - an image of an image. As an example, consider the diagram below for an object placed between two plane mirrors that make a   angle. Images   and   are primary images formed by the two plane mirrors. Image   was found by reflecting image   across the extension of the top mirror. And image   was found by reflecting the image   across the side mirror. The process can be repeated to determine the location of an image of an image of an image.

With two plane mirrors oriented at a nearly   angle to one another, six different images are formed of an object. When the two mirrors are aligned at a  angle with each other (i.e., a parallel mirror system), there are an infinite number of images. Each image is the result of an image of an image, or an image of an image of an image or an image of an image of .The diagram below shows the multiple images for a parallel mirror system. Images  and  are primary images. Image   is the image resulting from the reflection of the object   across mirror  and image   is the image resulting from the reflection of the object   across mirror.  Image   is an image of image , found by reflecting image   across mirror . Image   is an image of image ; found by reflecting image   across mirror . This process could continue indefinitely, producing images of images for an infinite number of images.