Why do SLRs use a pentaprism instead of a periscope?
To see the image the right way around and the correct way up in the viewfinder, there must be an even number of lenses and mirrors in the light path. This is because mirrors invert the image laterally and lenses that form real images give inversion both laterally and vertically.Think about turning an object upside-down: do it twice or four-times (any even number) and it ends up the right way again. A periscope has two mirrors and there is one camera lens – that gives a total of three (the viewfinder’s eye-piece lens acts as a magnifying glass and does not invert the image). The pentaprism ensures that the there is an even number of lateral and vertical inversions to give the correct image. Additionally: the penta-prism uses “total internal reflection” off the inside of the glass and these internal surfaces cannot be contaminated by dust, etc.