The fallacy of 35mm "equivalent focal lengths"

Started 3 months ago | Discussions thread
OP Tony Beach Forum Pro • Posts: 11,926
Re: The fallacy of 35mm "equivalent focal lengths"

thinkinginimages wrote:

Tony Beach wrote:


Ironically, even here at DPR equivalent focal lengths are often divorced from a complete understanding of what is or isn't equivalent. There is this idea that if a lens covers a certain FOV on a given format then it is somehow equivalent to whatever focal length that would cover that FOV on a 35mm format camera.

[This is a good place to suggest to anyone that doesn't want to read a long post (I usually don't like reading long posts) that you might want to skip to the picture below and take a long look at it and draw your own conclusions. Just be prepared for me alluding back to the "Getting into the weeds" portion of this post if you have any questions or concerns about what I'm presenting.]

The reason for this post is that I got to thinking about "reach" the other day as I was researching a compact camera to give my girlfriend for her upcoming birthday. “Reach” is one of the factors I was considering, and I’ve settled on a Panasonic Lumix DC-ZS70 with (among other features I think will be valuable to have) its 20 MP sensor and a 30x zoom. However, I don’t for a minute buy into the “24-720 mm equivalent focal length” which is how the camera is marketed (for instance, here and here). Will this new camera get more reach than the Canon PowerShot S95 it will be replacing? Undoubtedly, but I will have more to say about that later this week when I have the new camera in hand. Will it get more reach than I have with my D800, NIKKOR 70-200/2.8 VR and TC-14eII? I'm thinking it should, but that too remains to be seen.

Getting into the weeds

There are three things that add up to reach:

1.) Optics -- which includes the actual focal length (and not the equivalent focal length), and just how good the optics are (I looked at a 70-300mm lens for my D800 and it was sent back because it didn't have any more resolution at 300mm than the 200mm lens focal length I already had).

2.) Pixel density -- which is essentially how many linear pixels in a mm of the image circle covered.

3.) Aperture diameter -- which is what true equivalence is all about. As it relates to reach small apertures have more diffraction, and because smaller apertures restrict light coming to the sensor the exposure ends up being noisier which in turn negatively effects resolution.

Given all of that, what is the actual “equivalent” focal length of the Canon PowerShot S95 compared to what I routinely get with my D800? After some testing with various lenses I concluded that at 35mm my NIKKOR 28-70/2.8D matches the longest focal length of my S95, so it's a third of the published 105mm "equivalent" focal length of that compact camera. I expect the DC-ZS70 to do better than the S95 with its 129mm lens rather than the 22.5mm lens on the S95, and with its 840 pixels per linear millimeter rather than the 490 pixels per linear millimeter on the S95.

Will the DC-ZS70 do better than what I get from my D800 with my longest current focal length? Well here's the math so far for the D800 compared to the S95:

At 35mm my D800 with its 204 pixels per linear millimeter beats my S95 at 22.5mm with its 490 pixels per linear millimeter. That's not true of all the lenses I tested, and some could possibly do even better, but I did test my old NIKKOR 18-70 DX kit lens and at 50mm it barely matched the S95. One might have expected the S95 having 2.4x as much linear resolution as my D800 at the sensor level would translate to its 22.5mm lens being equivalent to a 54mm lens, and while reasonably close to that it's only 65% of the way there (35mm rather than 54mm). Some of this is about optics, for sure; but as I will show in the visual examples below diffraction is also a factor.

Maybe I should break out my D300 and crop its final output to 4:3 aspect ratio, which would work out to 10.8 MP and be a bit closer to the 9.98 MP for the S95, but at 181 pixels per linear millimeter that's only a difference in linear resolution per millimeter of 12.5% more for the D800 (i.e., it's barely noticeable). The thing is when it comes to focal length equivalence (if you define that as reach rather than FOV coverage area) is that it's not about the sensor's format or aspect ratio, it's about the relative pixel densities -- so if I put one of my 105mm focal length lenses on my D300 you're going to have a hard time at the pixel level telling the difference between its output on that camera and its output on my D800 (the one thing that will be obviously different will be the FOV, but that's not reach).

Given all of that, I'm expecting the reach of the ZS70 at about 105mm to beat my current longest lens on my D800. I'll try to test that hypothesis next week. In the meantime...

A picture is worth a 1000 words (if not more)

Okay, so now comes the visual evidence to back up what I'm writing about here:

As always, it's important to view this at its "original size" or "100% zoom."

My final thoughts (for this post)

For me that upper right crop at f/22 says a lot. Why? Because the aperture diameter at f/22 for a 90mm lens is 4.09mm, and that's (essentially) the same aperture diameter as f/5.6 for the 22.5mm lens used on the S95 (4.02mm). The middle crops are basically "web size," which in this context is the full frame of the S95 file and the equivalent FOV of the D800 file both sized to 1080 vertical pixels in height -- and for all practical purposes that's enough for a lot of people, and if that's the case I could probably have taken a good 20mm lens and gotten "good enough" results on my D800 under these conditions.

Well written. In a big overview I think "equivalence" created more confusion than it was worth. Taking the sensor and "mechanics" out of the equation, it's more about magnifications, and angles of view, the optics. What does 20X mean in common terms? Why equivalence in 35mm terms? It's such an old point of reference. (Been there.)

I use MFT. I don't think "2X (or 1/2) equals 35mm, so...". 14mm is wider, 150mm is narrower, 20mm is close to the human eye, etc. I'd lose my train of thought if I had to calculate every sensor size.

Thank you for that. My proposal would be to simply say in degrees the AOV of the lens.

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