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I don't understand why pentaprisms are needed to reflect light from the image up through the viewfinder. When I read why it is used, the explanation seems to indicate that it ensures the light coming up is reflected out the viewfinder at 90 degrees. But wouldn't a 45-degree flat mirror accomplish the same thing?

  • @scottbb I saw that one but didn't get it. "It's important to realize that you don't actually look directly through the lens with an SLR!" Aren't we though? "If you did, a periscope style arrangement would do just fine" So why not? "What you are actually doing is looking at an image projected onto the focussing screen by the lens." Isn't this the same thing? The image we're seeing bounced up off the mirrors? "This image is flipped left/right and up/down by the lens, and then up/down again by the main mirror." What's the "main mirror" here and why is it flipped this way? – John Kip Jan 24 at 21:52
  • I am looking at diagrams such as i.stack.imgur.com/P1gz0.jpg – John Kip Jan 24 at 21:53
  • Even in a periscope, the incident light is still the correct orientation after bouncing off the two mirrors and I don't see why it wouldn't work the same way in a camera like the diagram above. Periscope: physics-igcse.weebly.com/uploads/1/3/4/3/13437876/873907750.JPG – John Kip Jan 24 at 21:56
  • here's a more instructive diagram: cdn-ep19.pressidium.com/wp-content/uploads/2019/03/Lens-4.jpg – scottbb Jan 24 at 23:01
  • Left-right inversion: upload.wikimedia.org/wikipedia/commons/thumb/3/3b/… (Technically six sides, interestingly). I can't tell what becomes of the light rays that hit the crease though. – Sean Hill Jan 25 at 14:19
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It's important to understand that the image through the lens is inverted in both the lateral (x ↔︎ -x) and vertical (y ↔︎ -y) dimensions. Mathematically, this is the same as a 180° rotation about the z-axis (optical axis).

Thus, the upright image entering the lens, after being refracted and focused, leaves the lens flipped both vertically and horizontally. In order to view the image correctly, some sort of lens or mirror arrangement will have perform an additional left-right and up-down inversion.

A periscope mirror system performs two up-down mirror inverions, leaving the output image the same as the input, meaning a periscope is merely a translation of the image, but does not transform the output image with respect to the input image.

If you used the focusing screen on an older look-down SLR (one without a pentaprism/pentamirror) or TLR camera, such as a Rolleiflex, you'd see an image that is correct top-to-bottom (i.e., the sky is at the top of the image in the focus screen), but is flipped left-right. That is because the 45° reflex mirror that aims the image vertically doesn't transform the image left-right. It essentially undoes the up-down inversion that the lens performs, leaving only the left-right lens inversion.

Thus, the image entering the pentamirror / pentaprism on top of a typical SLR or DSLR is correct top-bottom, when viewed looking down onto the focusing screen. But if you were cut a periscope in half and look down onto the first mirror, the image would be inverted top-bottom (but not left-right).

So the difference between a periscope system, and a reflex mirror in the body plus pentaprism/pentamirror to the viewfinder, is that the pentamirror includes an extra up-down inversion to produce an image that vertically correct, as compared to the periscope system, which expects a correct image entering the periscope system.

Note: In reflex cameras, the pentaprism/mirror is also a roof style mirror, that performs a single left-right inversion in the middle of all the bouncing around. Essentially, one of the reflective faces in the pentaprism/mirror system is actually not a single reflective surface, but an inside corner of a 90° angle that bounces the light laterally, as well as vertically. I guess you could say technically the prism/mirror is no longer penta-faced and more hexa-faced. But I like the existing nomenclature of roof pentaprism to denote that the main light path is inside a 5-sided polygon, with the addition/adjective of the roof feature which accomplishes a secondary goal of fixing the image in the left-right plane.

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    One thing none of the diagrams commented in (and none that I've seen) do well is show the left-right transformation. – Hueco Jan 25 at 1:00
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First you have to swap left/right from the focusing screen (a matte surface since the viewfinder needs to display a 2D image and not a 3D one or you could not figure out whether the camera is focused as your eye could accommodate to the distance). And a pentaprism uses total reflection inside, so in contrast to the lighter pentamirrors it does not lose light for the three reflections inside.

  • Sorry, I don't understand this answer or how it addresses my confusion. I don't see where this left/right switch is happening or why it's happening at the focusing screen (isn't this screen blocked when we're not taking pictures anyway?). Also a pedantic counterpoint but doesn't reflection technically always lose light even if just a very small amount? – John Kip Jan 24 at 21:58
  • @JohnKip Yes, every time light interacts with any surface, there is loss of light intensity. That's just the nature of physics. The loss itself doesn't really matter — it's just something that happens on the way to the goal of capturing the image. It's like water wheels in a stream: very little of the energy of the moving water is converted to mechanical (and probably electrical) energy. Regardless, that doesn't stop us from using the water to power rotational motion where we can. – scottbb Jan 24 at 22:58
  • @JohnKip Have you ever used a magnifying glass as a toy camera lens to focus an image on a piece of paper/card/wood/wall? I used to do that a lot as a kid. The image generated by camera lenses is upside-down and flipped left to right. That's the natural image of a camera - flipped around/rotated 180 degrees. Using mirrors will not change the original image thus you'd see the flipped image in the viewfinder. The prism is to rotate/flip the image back upright. It is a GUI fix – slebetman Jan 25 at 17:20
  • @johnkip The focusing screen is not the image sensor! The focusing screen is located above the reflex mirror. It shows the image produced by the lens system like it would be on the sensor. It is this image you look at through the viewfinder. – Dubu Jan 26 at 16:43

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