How Sensor Size, Focal Length, Distance and Subject Size Relate to Each Other

Eyelight

Senior Member
Note: I think I have this worked out, but that does not mean it makes sense or that it is a perfect explanation. The diagrams are based on real numbers, but the math is absent to protect the innocent (keep it visual). I started fiddling with the diagrams the other day, but my Cadd software crashed and then Glen ran out of popcorn.

BIG NOTE: Let's leave specific cameras and pixels out of this thread. All we are dealing with is the four measurements and how they interact.

Sensor Size, Focal Length, Distance and Subject Size

These four measurements work together. Using any three you can determine the fourth. Changing one of the four will require changing at least one of the other three. Since we are mostly interested in FX and DX formats, we will use them, but the same applies to larger or smaller sensor sizes.

There is a point in a lens where light rays converge (it's more complicated than this, but thinking of it as a point will help with the basic ideas here presented). This point divides our measurements into two halves, before and after. It is the angle of view that ties the two halves together.

Sensor size and focal length determine angle of view. Angle of view and distance determine subject size (or view). This diagram shows how the four measurements come together using an FX sensor. The angle of view used is that of a 50mm lens.
FX Sensor FL FD View.jpg
What if we use a DX sensor with the same lens (same focal length) at the same subject distance? The DX / 50mm combo will see a smaller subject size.
DX FX 50mm same distance.jpg

What if we want to keep the same focal length and the same subject size? The DX / 50mm combo has to move to a greater distance.

DX FX 50mm same view size.jpg

What if we want to keep the same distance and the same view size? The DX sensor must use a shorter focal length lens to increase the angle of view to equal the angle of view of the FX / 50mm focal length combo.

DX FX same distance and view.jpg
 
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sonicbuffalo_RIP

Senior Member
The first three look good...I keep getting confused on the fourth scenario, but it's probably just me....I'll re-read it again! Nice charts!

Ok....I get it now....I'm slow....
 
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WayneF

Senior Member
There is a point in a lens where light rays converge.


All very well done, but this one sentence could be worded better (maybe "can be thought of as converging". Or maybe "is thought of", which is what you in fact are doing.) The sentence is true of a simple one element lens, like a magnifying glass. It could be assumed true of your hypothetical concept. Just not sure it should be said to be true. :) Because our camera lenses are more complex and are built slightly differently. You shouldn't change your pictures, but maybe this one sentence could hedge about it. :)

Lens designers can control the location of these "nodes" (using lens elements), and there are two nodes. The "triangle" from the subject plane is one (lets call its intersection node h), and the "triangle" from the sensor plane is a second node (let's call it h'... both shown in diagrams below). Those two fields of view are at equal opposing angles (as if they were the same one node), but the nodes are never in the same place. The lens elements sort of "relay" the signal between the internal nodes, from one to the other. I think same place is impossible in a multi-element lens. Except for macro distances, there is not much practical difference in the numbers of your examples.

But, it is a very big conceptual deal that they are different nodes, and there are strong advantages of two nodes NOT in the same location. For example, the definition of a telephoto lens is not necessarily a long focal length, but instead the actual definition of telephoto is a lens that that is shorter than its focal length. This specifically means point h' (focal length) is just outside the front lens element. So the lens is shorter (easier to carry and use). Your 200mm lens will not be as long as 200mm/25.4 = 7.87 inches from focal plane mark at rear of camera body. The word telephoto specifically refers to the moving of the node to a distant point (even if that meaning is about lost today).

A wide angle lens might be say 12mm focal length. But the FX frame is 24mm tall and the DX frame is 16mm tall, and both mirrors need room to be raised (mirror at 45 degrees is taller). A conventional 12mm lens would block the mirror (there were some very short fish eyes that did block it, mirror had to be locked up). So the typical WA lens instead puts point h' far behind the rear glass element, so the lens can be mounted well forward of the mirror, and the mirror is not blocked.

Here are diagrams which show this, from an old 1967 Nikon Handbook. I don't think the word Zoom is mentioned in this book yet. :)

mike1.jpg
 
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Eyelight

Senior Member
@WayneF

Your point about the point is a good point:), and I thought about wording it differently. But for the average user to gain a better understanding, I purposefully shied away from delving too deep into the science behind the magic.

I added a little caveat to the sentence to make the reader aware that more science is there if they want to pursue it.
 
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