Mirror reflections go on forever

Reflection of light¶

Objects can reflect part of the light falling on them, depending on the material and type of surface. This process is called reflection.

If (almost) all of the light falling on an object is reflected, one speaks of a reflection. Depending on the shape and structure of the reflective surface, a distinction is made between flat and curved, as well as between smooth and rough mirrors.

The plane mirror¶

Any smooth, flat surface (for example, a smooth metal plate, a calm surface of water, a window pane, etc.) acts like a flat mirror. While a brightly polished metal surface reflects all of the incident light, only part of the incident light is reflected from glass or water. Glass mirrors are therefore usually painted black on the back or provided with a light-opaque, dark layer.

The law of reflection

The law of reflection applies to plane mirrors: Every incident light beam leaves the mirror at the same angle as it hit.

The angle of incidence and the angle of reflection are given based on the perpendicular to the mirror. Mathematically, the law of reflection can be formulated as follows:

If you swap the location of the eye with the location of the light source in the images of the law of reflection or image creation on a flat mirror, the test result does not change. In general, the following applies in optics: Each ray of light can always travel its way in the opposite direction.

Image creation on a flat mirror

A mirror shows an image of the objects that are in front of the mirror. The resulting image can be constructed graphically using the law of reflection (preferably with a ruler and protractor).

Rays of light emanating from one point of the object , go out, hit the mirror at different angles of incidence and are thrown back according to the law of reflection. Some of the rays reach the observer's eye. If these rays are lengthened in a straight line towards the rear, they intersect in a pixel behind the mirror. For the viewer, the light that falls on the eye seems to emanate from this point.

Overall, the following applies to plane mirrors:

  • The object and its image are symmetrical to the mirror surface.
  • The picture is as big as the object.

Every pixel is therefore just as far behind the mirror as the matching object point lies in front of him.

Direct and diffuse reflection¶

The reflection of light rays on a flat, smooth mirror is called direct reflection. However, if light rays hit a flat mirror with a rough surface, one speaks of a diffuse reflection: The light is reflected ("scattered") in different directions, as shown in the figure Direct and diffuse reflection (right picture) according to the law of reflection.

A well-known example of diffuse reflection is the dull sheen of metal surfaces that have not been polished to a bright finish; Finely distributed water droplets in the air (clouds, fog) or ice crystals in the snow have a similar effect. The smaller the individual mirror surfaces of a rough surface, the more the light is scattered - often there is no longer a mirror image at all.

Curved mirrors¶

If the mirror surface is curved, the law of reflection applies to every single point of the mirror. A good idea for a curved mirror is a disco ball, which with numerous small mirror surfaces reflects the incident light spherically into the room.

In order to be able to describe the creation of the images on a curved mirror, the following terms are used:

  • Vertex:

    The center of the reflective surface becomes the vertex called.

  • Optical axis:

    The straight line that runs perpendicular to the mirror plane and goes through the vertex is called the optical axis. All rays that run parallel to the optical axis are called parallel rays.

  • Focal point (focus):

    All parallel rays hitting the mirror are reflected in such a way that they intersect at one point. This point lies on the optical axis and is called the focal point (focus) .

    The distance from the focal point to the vertex becomes the focal length called. In the case of a spherical concave mirror, the focal length is equal to half the distance between the midpoint and the vertex :

  • Focus:

    The middle-point the circle from which the curved mirror can be thought of as being cut out also lies on the optical axis. Rays that go through the center on the inside of the circle are always mapped onto themselves.

Depending on which side of a curved mirror is facing the light, a distinction is made between a curved mirror and a concave mirror.

Image creation on a curved mirror

A curved mirror (also known as a "convex mirror") always produces upright, reduced images. If an object is brought closer to the mirror surface, the image of the object becomes larger, but remains smaller than the original.

Objects are depicted by curved mirrors as if they were located on a smaller scale inside the mirror. In order to determine the location of an image point, the image rays emanating from the corresponding object point are drawn on the back of the mirror. It must be noted that rays incident in parallel always come to the focal point to be deflected and rays through the center go straight through the mirror. The position of the image that results when looking at the curved mirror corresponds to the point of intersection of the focal and center ray.

Since the images of a curved mirror are not only upright and scaled down, but also correct laterally, they are often used (for example in road traffic) to survey a larger area. They even allow a “look around the corner”: Regardless of whether you are looking at the mirror from above or below, the light rays always seem to come from the reduced image of the candle on the back of the mirror.

Image creation on a concave mirror

In the case of a concave mirror, the location and size of the image that appears depend on the distance between the object and the vertex of the mirror:

  • If one approaches an object from the focal point of a concave mirror, the image also approaches the concave mirror. Concave mirrors produce enlarged, upright and reversed images of the objects when they are within the focal length.

    To construct the image, one draws the image rays emanating from an object point in the opposite direction. It must be noted that focal point rays become parallel rays and central point rays always hit the mirror perpendicularly and are thus mapped onto themselves. The position of the image corresponds to the point of intersection of the extended parallel or central ray on the back of the mirror.

    Because of their magnifying effect, flat concave mirrors (with a large focal length) are used, among other things, as cosmetic mirrors.

  • If an object is approached to a concave mirror from a great distance, the image moves away from the concave mirror: Concave mirrors produce reversed, reversed images of the objects if they are outside the focal length.

    In turn, the focal point and parallel rays emanating from a point on the object are sufficient for the construction of the image, which in turn are mapped onto parallel or focal point rays by the concave mirror. The point of intersection of the reflected rays corresponds to the position of the image.