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Ever since I've heard of extension tubes I've been curious if they somehow crop the image that appears on the camera sensor.

Based on this YouTube video, the answer is "no" (at least not that I can tell).

Now that I know that, why not?

It seems like they would somehow muck up the image that appears on the sensor, and while they obviously do alter the DOF, it looks like the image still appears on the entire sensor. Obviously my understanding of how the lens forms an image on the sensor has something wrong with it, but what is the actual effect on the light when using an extension tube?

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The extension tube does change the field of view. Specifically, it enlarges the image circle size at the sensor/film plane. Light as it is projected by the rear of the lens onto the film/sensor plane is like the light coming out of a projector: the further away the screen is, the larger the image that is projected. Since the sensor/film does not expand as well, the angle of view is reduced as a smaller percentage of the total image circle is now falling on the sensor.

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    Extremely well put. – Itai Aug 21 '16 at 17:43
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    Ooooooh. So it doesn't reduce (in area) what's hitting the sensor, it increases it. And that's because it looks something like (lens)<|film/sensor so by moving the lens further away, the opening of the < gets bigger. Naturally, the light that used to fall on the edges of the sensor now gets partially absorbed by the tube and doesn't make up image. Is that right? – Wayne Werner Aug 21 '16 at 20:34
  • More or less. Most of the extra light circle probably lands on the sides, top, and bottom of the camera's light box rather than the sides of the extension tube. – Michael C Aug 21 '16 at 23:13
  • @WayneWerner You may find it easier if you read about first-order ray diagrams, such as this tutorial spie.org/Documents/Publications/00%20STEP%20Module%2003.pdf . Start perhaps with Section 3 to see how an image propagates thru several lenses. – Carl Witthoft Aug 22 '16 at 11:37
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    @CarlWitthoft that's actually the understanding that I already had from my college physics course. And as Michael points out, also probably why I had a mistaken intuition about how an extension tube works. – Wayne Werner Aug 22 '16 at 12:12
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The camera lens acts just like a slide or movie projector lens in that it projects an image on film/sensor. The camera lens actually projects a circular image that is quite a bit larger than film/sensor. Only the central portion of this image circle is usable. The outer limits of the image circle are dim (vignette) and have soft focus. Only the central portion of this projected is photographically useful. The central part of the image is called “The Circle of Good definition”.

The diameter of the circle of good definition increases as the lens is racked forward. In other words, the lens to film/sensor distance is at its closest when imaging objects at infinity (∞ as far as the eye can see). As we focus on objects that are closer than infinity, the distance lens to film/sensor lengthens. As we close focus to obtain “unity” (life-size, magnification 1, 1:1 etc.) the lens is racked forward. Now the distances between lens and image is twice the focal length. Additionally, the distance between lens and object is also twice the focal length. The total distance object to image is 4X the focal length. When unity is achieved, the circle of good definition is now twice the size as compared to the infinity position.

OK, the circle of good definition increases as we close focus. Now we must pay attention to the diameter of the extension tubes. If they are too small the corners of projected image will be lopped off (vignette). As a rule of thumb, extension tubes are sized for use with the “normal” lens. A “normal” lens is one with a focal length about equal to the diagonal measure of the format frame. The full frame (FX) measures 24mm height by 36mm length and the diagonal measure is 43.3mm. By convention, the “normal” lens has a focal length rounded up to 50mm. This lash-up delivers a field of view 46⁰ computed in terms of the diagonal. Additionally the circle of good definition just covers the diagonal corners of the frame. It takes special design considerations to make shorter lens that will cover this frame size without vignetting. This is a key ingredient as to why the 50mm lens is considered “normal” for the FX.

Let me add that extension tubes are usually designed around the “normal” lens. If you mount a longer lens, you likely will get some vignetting.

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