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The question of how lens focal length and binocular magnification appears to have been asked over 3.86 quinzillion times. Regardless, it's still hard to get an answer the layman can understand. I'd like to have another go by asking a very specific version instead of the more general question.

Here goes:

  • I'm into back-yard birding, for which I currently use a pair of 8x magnification binoculars (Nikon Monarch M511 8x42 6.3° to be precise), and I now want to add bird photography to my activities
  • I already have a camera in the form of a Nikon D5200. I believe its sensor has a "crop factor" of 1.53 (and I am led to believe that number is important)
  • So, I'd like to obtain a lens that I can use with my D5200 so I am able to see a bird in at least as much detail (i.e. magnified at least as much?) as I do when I look at it with my binoculars, specifically in the following two situations:
    1. When I look at it through the viewfinder of the camera
    2. When I look at it in the end photograph

Some other (possibly) relevant info:

  • My primary interest for now is observing the bird and recording its image; i.e. it is not in producing aesthetically pleasing bird-ish art. And so specifically, I don't care about depth of field -- or, rather, I don't care if I cannot achieve a shallow DoF. (Do I?)
  • I live in a region with very bright sunny days, and most of the birds I'm concerned with are stuffing their fat asses with food from my feeders, so they're not exactly in a hurry. In other words, the speed/aperture of the lens isn't that important. (Is it?)
  • Of the two aspects of my lens requirements -- looking through the camera viewfinder, vs looking at the end photograph -- the first is more important to me (because when it's live, through the viewfinder, it might fly away, so the more detail the better; once I've taken the shot, less detail is compensated for by now-unlimited time in which to study it)

So, given all of that, my main question is simply:

Q1. Which focal length of lens do I need?

If I could get a straight and simple answer, ideally in the form of a number of millimeters, that would be WONDERFUL. Provide it and you may consider yourself a candidate for the next Nobel Prize in Straight and Simple Answers on photo.stackexchange.com (it's going to be huge!), or at very least a Truly Wonderful Being.

HOWEVER, based on reading the countless other attempts to ask this kind of question, and their answers (OK, I admit I may only have read 10 to 20, but there are a lot), I accept that in the underlying optical equations there are umpteen other variables over and above just focal length, so in case it's simply impossible to answer Q1 based only on what I've told you so far, here is a followup:

Q2. If my description does not provide enough information to answer Q1, is it possible to specify (and if so, could you so specify) what else you'd need to know to enable an answer?

For example, does it matter how far the birds typically are from where I observe them? Does it matter if I first chuck a brick at all the boring old White-winged Doves so as to clear the way for the spectacular Painted Bunting I actually want to see?

Finally, a pragmatic closing question. I'm pretty sure the number I'm looking for is something in or around the 300mm to 400mm range and for me that might represent a bit of a price pain point: 300mm or less is OK; 400mm or above is a bit ouchy. Therefore:

Q3. If the answer to Q1 is something above 300mm (e.g. 428.4mm if I had to take a rough guess), and I decided I just couldn't stretch that far, just how inferior to my 8x42 binoculars would that 300mm lens's image be, especially in the all-imporant how-it-looks-live-through-the-viewfinder department?

P.S. In case there are any Brit birders reading this, especially fans of Bill Oddie, yes, yes I know that for identification purposes it's better to learn to draw the wee buggers rather than to take pics of them, but I draw the way Hoopoes congregate in Trafalgar Square, so I want a lens!

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According to Nikon, the D5200 has a viewfinder magnification of

Approx. 0.78x (50 mm f/1.4 lens at infinity, -1.0 m-1)

This means a magnification such that the image of an object you see when looking in the viewfinder would be the same size as looking at that same object with your naked eye would be with an approximately 64mm focal length. To get the same 8X magnification you get with your 8x42 binoculars you would need a 513mm lens.

With a 300mm lens you would get roughly 4.7X magnification at the viewfinder compared to looking at the same objects at the same distance with your naked eye.

Note that with a 1.5X crop body, the diagonal angle of view rendered with a 513mm lens would be around 3.5°, so to get the same magnification factor as you look through the viewfinder, you'd give up quit a bit of field of view. This is because the exit pupil of your D5200's viewfinder is smaller than the exit pupil of your 8x42 binoculars with a 6.3° AoV. That 300mm lens, on the other hand, would give you about 5.5° diagonal angle of view.

In other words, the size of the circle you see in your binoculars would have almost twice the diameter as the diagonal of the rectangle you see in your camera's viewfinder. (This assumes the eye relief, or the distance your pupil is placed behind the exit pupil, is the same for both.)

For more about how focal length, sensor/focusing screen size, and viewfinder magnification interact to affect the size of objects when viewed through a viewfinder, please see this answer to Can I convert binocular zoom to equivalent lens focal length?

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    Just revisiting to mark this as answered and to say thanks @Michael Clark. As of yesterday, and after a couple of months of agonizing and comparing, I now sit grinning with my brand new Tamron SP 150-600mm F/5-6.3 Di USD G2. And there was me thinking, back in May, that I’d get away with spending a few hundred bucks on a used 300mm or thereabouts 😀 Thanks for the advice, here and in your other answers.
    – tkp
    Jul 15, 2018 at 13:58
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The astronomical community has posted several on-line calculator that they use to compare telescope and binocular power to magnification obtained when a camera is mounted at prime focus. I checked several and found that they are based on a lens with a focal length equal to the diagonal measure of the image sensor equals magnification 1. I found this the case, testing the programs using different size formats. Thus for a compact digital 16mm height by 24mm length, 30mm is the diagonal measure. If true, and I believe it is, than 30 X 8 = 240mm focal length compares well to your 8X binoculars. .

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  • If that were true, then the viewfinder magnification of the Nikon D5200 using a 50mm lens would be 1.67X rather than 0.78X as Nikon publishes it. Perhaps your formula is based on magnification of an assumed print size rather than the view from the exit pupil of the camera's viewfinder? Not to mention that two cameras with the same size sensor and different viewfinder magnifications will project different sized exit pupils of the same image projected by the same lens on the same sized focusing screen...
    – Michael C
    May 14, 2018 at 6:40
  • @ Michael Clark -- It’s easy to check using an SLR. Mount the camera so that one eye is peering through the viewfinder while the other eye, kept open, is viewing the same vista. This is a common technique, especially appreciated by sideline sports photographers who adore being clobbered when working football games. Anyway, you can zoom and match the size of objects until they juxtapose. At what focal length will the juxtapose occur? Depends on power of the eyepiece lens of the viewfinder. I found that a 58mm on my Nikon F yielded magnification 1 for the viewfinder view.
    – Alan Marcus
    May 14, 2018 at 15:55
  • Yep, and it takes a roughly 65mm lens to get that on a D5200, so how can 1X magnification be at 30mm? The question specifically asks what focal length is needed to get 8X magnification through the viewfinder, not onto the sensor and then enlarged to some arbitrary print size.
    – Michael C
    May 14, 2018 at 18:12
  • Alan; useful tip but sadly not for me or anyone else with Amblyopia 😀. Or maybe that should be 🤪 since my lazy eye was caused, as is common, by childhood Esotropia. In fact, I remember when I was little doing an exercise similar to what you recommend, during many a boring session at the eye surgeon’s. I had to sit at a machine and try to make the right-eye image of a sentry align with the left-eye image of a sentry box. It never “took” and I now have optically excellent right-side vision that cannot be corrected to better than 20/80 because its neural circuitry is a pile of wet noodles.
    – tkp
    May 16, 2018 at 11:40
  • @ tkp - Have a friend, with two good eyes, help you.
    – Alan Marcus
    May 16, 2018 at 13:44

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