What is effective focal length after cropping? SAT-like question.

[Daniel Browning]

My 5D Mk II put out a JPG with these dimensions: 5616x3744 pixels. If I crop it down (same proportions and not resizing) to where the final image is 960x640 pixels, that is as if I had a ???mm lens.

The 35mm-equivalent focal length is 1170mm (crop factor is 5.85X). Here's how you calculate it:
crop factor = 5616 / 960
35mm-equivalent focal length = 200 * crop factor


It is almost exactly the same as using a smaller sensor. In fact, a 960x640 crop from the 5D2 (6.1 x 4.1mm) is about the same size as the sensors in most compact digicams (e.g. DMC-FZ150). The FZ150 lens only goes to 105mm though, so you'd have to crop the digicam down from 12 MP to 4 MP in order to get the same field of view as the 5D2. Of course, 4 MP is a whole lot more than 0.6 MP.

That is just like having a bigger lens.

Well, it's like having a longer, slower lens. It's like an optically perfect teleconverter.


A 200mm f/2.8 lens on a teeny tiny 6.1mm sensor (which is what your 5D2 is after you crop it down to 960 pixels) is equivalent to a 1170mm f/16.4 lens on the 5D2.

OK, for additional points, if I did the same using a 500mm lens and a 105mm lens, what would the effective focal lengths be?

First, let me rant a little bit about the word "effective". There is an important difference between "equivalent" and "effective". Let me illustrate with some examples:


* A tiny boat requires 10 horsepower to go 10 MPH.
* A large cruise ship requires 100,000 horsepower to go 10 MPH.


Now, which of the following is correct?


* The engine on the tiny boat is effectively 100,000 horsepower.
* The engine on the tiny boat is equivalent to 100,000 horsepower on a cruise ship as it pertains to MPH.


Here is another example:


* To fill my field of view, I sit 5 feet away from a 10-foot-wide display.
* To fill my field of view, I sit 50 feet away from a 100-foot-wide display.


Which of the following is correct?


* If I sit 5 feet from the 10-foot-wide display, it effectively becomes 100 feet wide.
* If I sit 5 feet from the 10-foot-wide display, it is equivalent to the field of view of a 100-foot-wide display seen from 50 feet.


Now with photography:


* "An 80mm lens on APS-C is effectively 130mm."
* "An 80mm lens on APS-C is equivalent to 130mm on full frame for angle of view."


The difference is important. Comparing two things (such as angle of view between formats) doesn't "effectively" change anything, so effective is not the right word to use. Discussing the "equivalent" is very useful, though.


Furthermore, in most lenses, the focal length printed on the lens is only true when focused at infinity. When you focus closer, the "effective" focal length changes. It may say 100mm on the box, but at nearest focus it is really only 85mm. Similarly, adding a teleconverter truly changes the "effective" focal length. Those are both cases where the focal length truly does change, so it would make sense to say "effective focal length" if you desired to make a distiction between the number printed on the lens and the actual property itself.


Friends don't let friends use "effective" ineffectively.


The reason why I consider it important is that I think using the word effective instead of equivalent causes a lot of confusion and misconceptions. Use of the term "effective" is very widespread, including Canon's own camera manuals, but I still think it's incorrect and misleading. Every new photographer who sees that term is going to assume the honest-to-goodness focal length truly changes. If we used the term "equivalent focal length" instead, then they wouldn't get that misconception.


We should reserve "effective" for cases where it is appropriate, such as teleconverters and lens breathing. Take these three examples:
The effective focal length of a 200mm macro focused to 1:1 is 170mm.
The effective focal length of a 200mm lens with 2X TC is 400mm.
The effective focal length of a 200mm lens on APS-C is 320mm.
To me, the first two are sensible and normal uses of the word effective. Internally-focusing lenses really do change the honest-to-goodness focal length when focusing. Similarly, adding a TC changes the focal length. Using the word "effective" here is useful to highlight that the actual focal length is not what you might expect -- it's different from the number printed on the lens. They're different from the third usage.

OK, for additional points, if I did the same using a 500mm lens and a 105mm lens, what would the effective focal lengths be?

Now, to answer your question, a 960px crop with a 500mm f/4 lens would be equivalent to 2925mm f/23.4. At 105mm f/2.8 it would be equivalent to 614mm f/16.4


Hope that helps.