# Optical 101:Corner Cube

The corner cube has the function of retroreflecting the incident light and returning it to the incident direction. The reflected image is inverted. Unlike mirrors that have retroreflective properties only at an incident angle of 0 °, the retroreflective properties of corner cubes are effective even at large incident angles. Taking advantage of this feature, it is frequently used when it is difficult to adjust the optical axis or when you want to shorten the work time. There are three reflective surfaces on the corner cube. In general, the maximum allowable incident angle at which total reflection of light can be obtained is theoretically up to 5.7 °.

## Usage of corner cube

It is used as a reflector for length measuring machines that use a laser. Developed to measure the distance between the Moon and Earth, it was installed on the Moon when the Apollo spacecraft landed on the Moon.

There are many things around us that take advantage of this property. Many very small reflectors are also accumulated on the red reflector attached to the rear of the bicycle and the reflector (orange or colorless) installed on the road or on the side of the road. Recently, smaller seal types are also on sale.

## Corner cube principle

There are two types, hollow type and prism type. Both have the same basic structure that utilizes reflections on three sides.

The three faces are installed so that they are orthogonal to each other. Let the three faces be the xy face, the yz face, and the zx face, respectively. For example, when light is reflected on the xy plane, the sign of only the z component of the three-dimensional vector component that indicates the direction of light travel is inverted, and the x and y components do not change. Similarly, the sign of the x component is inverted for the yz plane and the sign of the y component is inverted for the zx plane. Due to this property, the rays whose incident direction vector is [a, b, c] are inverted to become [-a, -b, -c] by being reflected sequentially on the three surfaces. In other words, it returns light in the direction it came from. There are a total of 6 combinations of the order in which the incident light is inverted, and it is determined by the position where the light beam is incident. As a result, the signs of all components are inverted regardless of the order of reflection.

Due to the "berration" caused by the relative velocity between the observation station and the artificial satellite, it is more effective to shift the orthogonality slightly than the reflector with the correct orthogonality. Many of the reflectors of artificial satellites actually used intentionally shift the degree of orthogonality.