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Assume that I have a camera obscura (with a large lens - something like a magnifying glass) setup projecting an image of some still life. I look at my projection on my projection plane and I see one specific perspective of the still life. Moving or rotating this plane around does not change the perspective, only the focus.

Now I remove the projection plane and place my eye a few steps back from where the projection plane was. According to the answers to my previous question, at this distance, my eye will see a virtual image of the still life inside the lens. If I move my head from side to side, I now see different perspectives of that same still life. For example, in this head position, the orange is completely covering the grape. Or, moving to this head position, the jacket in the background moves from the right to the left side of the bowl.

Why are these different perspectives possible, when all the light entering my eye is a sample of the same light that created the one-perspective-projection? Should not my eye just see different parts of the still-life image when I move my head around, and not different perspectives as well?

  • @bogl I am using a large lens from a magnifying glass. I have observed seeing many perspectives actually. It is easily reproducible if you have a magnifying glass lying around. My question is prompted from trying this in real life and not understanding why. – natsuki_2002 Jan 3 at 16:49
  • Just like in your other question, the answer is that your premise is wrong: A projection screen and your eyeballs are not interchangeable optical systems. Your eyeballs are more like a camera, i.e. a lens + projection screen. The magnifying glass and the actual projection screen together is yet another camera and comparable to your eye as a whole. But if you now take that other camera's lens (the magnifying glass) and strap it in front of your camera (your eye), you create something entirely new that doesn't compare (optically) to what you had before. – null Jan 3 at 18:39
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  • Perspective is only defined by the location of the viewing point.

  • The Camera Obscura projects the scene through a pin hole of very small diameter. All light rays are going through the pin hole. The pin hole alone defines the viewing point.

  • A pin hole does not create a virtual image. If you look at the pin hole with bare eyes, you will only see a point of light. The angle and distance from the pin hole to your eye does not matter (as long as you are inside the Camera Obscura).

  • Your setup differs from a Camera Obscura because you are viewing through a lens of significant diameter. The left and right edges of your magnifying glass are distinct different viewing points, defining different perspectives.

  • If you project through that lens to a screen, only those points in focus are projected like with the Camera Obscura. (points are in focus when 1/a + 1/b = 1/f, a: distance object to lens, b: distance screen to lens, f: focal length of lens). The perspective and the viewing point are defined by the center of the lens. With a large aperture, out-of-focus points of the scene will appear blurred on the screen. Also note that the apple is partially obstructed. The whole apple is only visible to some parts of the lens, changing the shape of the blurring.

enter image description here

  • It becomes a different story when you remove the screen and watch through the glass with your bare eye. The magnifying glass and the lens in your eye together form an optical system. The viewing point is defined by both - magnifying glass and eye. It will be somewhere between them. Thus the perspective will change when you move either glass or eye.

    Looking with the eye (small lens) through a big lens

    Note that

    • many light rays (like the purple lines) never hit the eye.
    • both objects appear pretty sharp, because the aperture is now defined by the iris in the eye, and is much smaller than the the aperture of the large lens.
    • the drawings above are just quick sketches. They are not meant to withstand academic scrutiny. In particular, I did not even try to construct the diffraction angles accurately.
    • in the second drawing only the center rays are illustrated, whereas the first drawing also shows two additional rays per object.
    • Our retina is curved instead of flat.
  • The notion of the virtual image creates a lot of confusion, but in your setup it is actually useful: The magnifying glass creates a virtual image of the object that appears closer to you than the object itself. When you move your eye, you change the view point and the perspective.

  • If the idea of the virtual image still confuses you, thinking of a flat mirror might be helpful: Stand in front of a wall mirror. The mirror creates a virtual image of the scene around you. That virtual image is located inside the wall. When you move your head around, the perspective is changing.

  • Thanks for your great answer! One thing that still confuses me. Assume, for example, using my eye to look through the lens that there is a head position where I can see both the orange and the grape, and then a second position where the orange covers the grape. If I setup a screen to project the image, and I see the orange covering the grape perspective, where are the light rays that contribute to form the grape image? Are they blurred out and help form some background bokashi? I know that they are passing through the lens since I can see them in another head position... – natsuki_2002 Jan 4 at 9:53
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    When the edges of the objects end your eye are aligned, you will see a thin blurry edge of the rear object next to the front object. The amount of blur depends on the aperture. Like when you squint your eyes, there will be less blur. But the vast majority of the light rays never makes it to your eye. They are just shining some light on you and your environment. I added two drawings - hope they help! – bogl Jan 4 at 13:28
  • @natsuki_2002 Remember that your eye contains a second lens and its own focusing system. A screen does not. Looking through the lens your second lens is able to focus on the objects and observe the parallax between objects on different planes. On a flat screen, these "perspectives" combine to provide the out of focus parts of the image. – LightBender Jan 4 at 13:41
  • @natsuki_2002 Also not that everything said here is going to be a gross oversimplification. Optical physics is a very broad subject involving everything from wave/partical duality to material engineering. – LightBender Jan 4 at 13:47
  • @bogl Parallax is certainly evident with two eyes and provides humans with the ability to detect depth, but parallax itself is just the apparent difference in the location of objects on different planes when viewed from different points. – LightBender Jan 4 at 13:53
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When you move your eye "a few steps back" (what is that supposed to mean?) from the projection plane, you see a virtual image. The depth of focus of that virtual image depends on your aperture. The kind of variation in object relation you imagine is possible to see obviously cannot extend beyond the variation of views from the front of the lens. That is a pretty small variation but it can mean that if you put two disks behind one another at significant distance such that the second disk is covered completely by the first disk viewed from the front of the lens, that if you now focus on the first disk, the defocusing blur from the second disk will be visible around the edges of the first disk even if the disk "proper" is hidden. Similar for focusing at the distance of the second disk: then its border may appear in the blurred outline parts of the first disk.

You cannot "change perspective" really: the excerpt that you are viewing is magnified so when you move to the side, you don't get a different perspective of the same scene but rather the same perspective of a different scene.

Try it. Where is the point in asking questions about things that you learn better by doing?

  • Thanks for your response. My question is actually prompted by me trying this out in real life and not understanding why. If you take a large lens like a magnifying glass. Set it up to view an assortment of objects in a room at different depths, bring your eyeball back behind where the projection plane of one of the objects would be, and then move your head around, you will see shifts in perspective - where those objects will go between being separate to overlapping each other. This is what I mean by perspective changing (maybe I'm using the wrong words?). – natsuki_2002 Jan 3 at 16:45
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When you move your head, you change the relationship between your head and the lens. The optical axis between your eye and the lens points in different directions when your eye moves. Thus the extension of that optical axis through the other side of the lens also moves.

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