Flat mirrors can be used to change the direction of a beam and to change the orientation of an image. But by making use of refraction and total internal reflection (TIR) it is also possible to use prisms of various shapes to reorient images.
Right-Angle Prism
The prism is used like a mirror. If the refractive index of the prism is large enough, we obtain Total Internal Reflection (TIR) and that the prism acts like a mirror of 100% reflectance.
How large must the refractive index be?
We want the critical angle θc to be smaller than 45 degrees. Since for a glass prism in air sinθc = 1/n, we need n > 1/sin(45o) or n > √ 2 = 1.414.
Dove Prism
This prism is used to "flip" an image without reorienting the optical axis.
Penta Prism
Like the Right-Angle Prism, this prism reorients the optical axis by 90°. However, the Penta Prism does not flip the image. Penta Prisms are used in 35-mm Single-Lens-Reflex (SLR) cameras to produce an upright image in the viewfinder.
In image forming systems prisms must be used in parallel light beams to avoid introducing defects into the optical image.