Pentagonal prism is one of the beam steering devices with fixed angle (90 °). It has two purposes: first, the outgoing light turns the incident light to a certain angle (90 °) regardless of the incident angle on the first side; Second, unlike a right angle prism, its image has neither rotation nor specular reflection. Pentaprism is commonly used in camera viewfinder, image observation system or measuring instrument.

## Basic concept of pentagonal prism

The characteristic of pentagonal prism is that the light is vertically incident from either side of the 90 ° angle, then reflected by the two sides of the 45 ° angle and emitted from the other side of the 90 ° angle. The incident light and the outgoing light are equal to the 90 ° angle. In this way, the optical axis can be turned 90 ° by using pentagonal prism. Recently, the planarity of large plane has been measured by using this characteristic of pentagonal prism [1], that is, when the pentagonal prism rotates around the horizontal axis, the outgoing light sweeps a plane in the vertical plane. On the contrary, when rotating around the vertical axis, the planarity in the horizontal plane can be measured. When the laser is used as the light source, a large plane can be swept due to the long range of the laser, which is very important for house construction The planarity measurement in large-scale engineering construction is obviously simple, convenient and high-precision, so the need for pentagonal prism is more and more.

Pentagonal prism cannot realize internal total reflection according to the principle of critical angle. Therefore, the two reflecting surfaces of the prism are generally coated with aluminum film and black paint, and its incident surface and emitting surface are coated with MgF2 single-layer anti reflection film, as shown in the figure.

## Basic characteristics of pentagonal prism

The accuracy of the use angle of pentagonal prism is related to 90 ° angle and 45 ° angle, as well as the material of prism. The angular error in the pentagonal prism that is consistent with the light is called the first parallel difference, and the one perpendicular to the optical axis is called the second parallel difference (i.e. tower difference). The error of the first parallel difference is equation 1, and the error of the second parallel difference is equation 2.

N is the refractive index of glass.

When studying the above error formula, since the first parallel difference is more important, the following problems are discussed:

(1) In the first parallel difference, there is a 2n coefficient before the 45 ° angle. It can be seen that the error of 45 ° angle has a great influence during processing. Therefore, generally try to process the 45 ° angle accurately;

(2) In the formula, 90 ° angle and 45 ° angle form a subtraction term, which obviously hopes that the error value symbols of 45 ° angle and 90 ° angle are the same during machining, so as to make them compensate each other and

The error value of becomes smaller. If the two errors are different, the error will increase;

(3) Since the error form is related to N, it is also necessary to pay attention to the change value of refractive index n of glass: for example, when n = 1.5, the error formula is

Due to the change of N, the influence on 90 ° angle and 45 ° angle is 1:6, which should be paid special attention to when selecting glass consistency, that is, high-quality glass with small change of refractive index must be selected.

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