Magnification of Binoculars vs. Lenses (1 Viewer)

[peaOP]

How do the magnification values on binoculars translate into lens focal lengths?

For example, if I have a pair of 5 x 21 mm binoculars (5x magnification with a 21 mm objective diameter) what would be the equivalent focal length of a lens to give me the same subject magnification?

The main problem here is the lack of a benchmark. What do we base a 1x magnification on? 50mm?

 

[OPTIC_NUT]

The magnification is basically the ratio of the objective's focal length to the eyepiece's focal length.

So....there isn't a a single lens that can replace that.

Regular magnifiers tend to break up and distort badly past 2-3x.
Loupes can get you to 10-20x but you have to cram your eye towards them.
Instruments give you not just magnification but practical distances.


1x, by the way, is you looking at the world with no lens at all. ;-)

So...unfortunately there's a lot of non-linear stuff that gets in the way of that comparison.

 

[typo]

Hi and welcome to the forum.

I'm not sure I entirely understand what you are asking here. Unlike a camera lens which forms on the film/sensor, a binocular forms an intermediate image internally which is viewed with a separate lens group in the eyepiece. The magnification is given by the ratio of the focal length of the objective to the focal length of the eyepiece. So your compact 5x21 might have a 50mm focal length objective and a 10mm focal length eyepiece.

You may have answered the question yourself in that there is a rough approximation of 50mm per times magnification for the 35mm sensor equivalent lens. So your 5x is roughly a 250mm lens equivalent.

David

 

[WJC]

Magnification is due mainly to the curves and spacings in the eyepiece. You might have a 7x50, 10x50, or 15x50 that all use the same objective.

Bill

 

[OPTIC_NUT]

Theoretically, that is a truism. A caution, though: keeping the exact same FL of the objective would result in
either an oddly narrow 7x view, a distorted 15x field, or some combination. When the length stay the same,
the mfgr has usually opted for the narrow 7x view. That's a low-cost product line.
To keep the lenses performing at their best, for example,
the 15x design likes to make life easier on the ocular by increasing the length. Pretty much as it works with
telescopes. You might have a 'rich-field' short 80mm or a 'high-power' 80mm with a longer barrel.

Typo: you are guessing the OP referred to some equivalent camera lens. You're probably correct.
It's hard to figure the equivalence nowadays. Back when the image plane was almost always
35mm and physical it was easier to compare.

 

[Bencw]

Magnification is due mainly to the curves and spacings in the eyepiece. You might have a 7x50, 10x50, or 15x50 that all use the same objective.

Bill

Now this is something that often puzzles me, (among many things !!) my understanding was like you say Bill, magnification mainly due to the eyepiece, but an earlier OP had replaced the eyepieces in a Swift 10x50 with ones from an Audubon 8.5x44, I asked if that now made it an 8.5x50 but he said no, due to the focal length it was still a 10x50 but with better eyepiece lenses.

 

[WJC]

Now this is something that often puzzles me, (among many things !!) my understanding was like you say Bill, magnification mainly due to the eyepiece, but an earlier OP had replaced the eyepieces in a Swift 10x50 with ones from an Audubon 8.5x44, I asked if that now made it an 8.5x50 but he said no, due to the focal length it was still a 10x50 but with better eyepiece lenses.

In optics, "one size," definitely, "does not fit all.

For example, there was a US Navy 7x50 binocular, from the war years, that came with a second set of objective housings (bells), which, when replacing the original 50mm housings with the new 63mm housings, made the instrument a 9x63.

There was almost always a slight problem with collimation, but, in a perfect world, the notion was sound.

Those exact powers, I mentioned were possible. However, the eyepieces had to be changed to match the f/l of the objective, to make it work out.

Cheers,

Bill (OMC) Cook

 

[OPTIC_NUT]

Practical idea, economically. If you go on the long side, f/l wise, it will stay sharp.
I wonder if the middle focusing lens in recent roofs gives them more flexibility...
you can use it to ease distortion a bit and act as a field lens.

 

[WJC]

"I wonder if the middle focusing lens in recent roofs gives them more flexibility..."

Yes, but any time you try to make something what it's not, the compromise slightly lessens the performance on either side. Still, if observer's saw OPD plots, of even the best binos, they would probably tone themselves down an octave or two.

Me, I don't care; it is what it is. I just enjoy what I have.

Bill

 

[peatmoss]

How do the magnification values on binoculars translate into lens focal lengths?

For example, if I have a pair of 5 x 21 mm binoculars (5x magnification with a 21 mm objective diameter) what would be the equivalent focal length of a lens to give me the same subject magnification?

The main problem here is the lack of a benchmark. What do we base a 1x magnification on? 50mm?

Hi TopeakTOP. Welcome to the forum! Are you trying to compare binocular magnification to lenses that one might use on a camera? If that's what you're trying to do, then I'm afraid that the answer is probably that it depends on the specific camera and the specific lens. If you took a lens with a focal length of 50mm, it might be considered to be a normal (1x ish) lens on one camera, but a long telephoto or even a wide angle on a different camera, depending on the specific camera's format size. Fwiw, my understanding is that when Nikon introduced their "F" slr in the 1950s, they paired it with a lens with a focal length around 55-58mm, because, with that camera's viewfinder, the resulting view had a true 1.0x magnification (so a photographer could keep both eyes open, one eye looking through the camera and the other eye staring towards the subject, and his brain could combine both images).

 

[Mark9473]

Camera lens magnification is calculated as lens focal length divided by the diagonal size of the camera sensor.
So a 50 mm lens on a 24x36 camera is giving 1.15x magnification; on an APS-C camera it's giving 1.86x magnification; on a 4/3 camera it's giving 2.31x magnification; on a 1" sensor camera it's giving 3.15x magnification, etc.

 

[OPTIC_NUT]

Awesome, thanks!

So: (50 / 1.15) = (BCL / 8(power example))

---cross-multiply and divide--

For 8 power...

SO: BCL (BinCamLen) = (50 * 8) /1.15 = 347 mm. (old camera equivalent)

That feels about right, having looked through 300mm telephotos eons ago.

But as you mention, sensor size throws a whammy into that.