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# Are binoculars achromats?

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### #1 Guest_**DONOTDELETE**_*

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Posted 29 February 2004 - 01:23 PM

Are the lenses in Oberwerk binoculars the same type as those in an achromat doublet refractor? I ask because I had assumed they were, but they look much different.

Also, if the answer to the previous question is yes, I’d like to know the focal ratio of the 15x70mm and 22x100mm binoculars. The best I can do is measure on the outside. Does anyone know the value? If not, do you have any information that would help me to get a more exact approximation, such as the distance the light travels from the prisms to the eyepiece, or a diagram of how the light travels through binoculars?

### #2 EdZ

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Posted 29 February 2004 - 10:59 PM

I've written a brief on how to figure this out. it's a section of an article. go here and look for the section "Focal Length"

Comprehensive Comparison of Four 70mm Binoculars

I actually took the entire prism shelf intact out of the 20x80 deluxe and measured the light path through the prisms as 130mm. For the 15x70's I estimated the prism light path as 110mm. the rest is explained in the article.

edz

### #3 Guest_**DONOTDELETE**_*

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Posted 01 March 2004 - 12:30 AM

Thanks a lot Ed!

### #4 Guest_**DONOTDELETE**_*

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Posted 02 March 2004 - 12:45 PM

I believe most objective lenses used in prismatic binoculars have focal ratio between f/3.5 and f/4. When estimating the prism light path, one has to divide the measured geometrical path of the prisms by the refractive index of the prism material to obtain the actual light path.

Also, it should be noted that cemented doublets used in binoculars are slightly different than those used in refactor telescopes. The binocular objectives must compensate for additional spherical aberration and longitudinal color introduced by the prisms.

Mike Rhee

### #5 EdZ

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Posted 02 March 2004 - 01:43 PM

bak4 glass has a refractive index of about 1.57.

the geometrical path through a set of large (20x80) prisms is actually measured at 130mm.

Could you please explain to me how the actual light path could be 130 / 1.57 = 83mm?

I have the understanding that because the light enters the prism face at exactly 90°, perpendicular to the glass surface, and exits the same way, the light is not bent. the refractive index of a medium would change the angle of the light as the light passed from one medium to another and if the light entered the medium at an angle other than 90°. It is bent at 90° when it hits the back of the prism, but in this case it has not yet exited the glass.

This seems to indicate to me the light path is equal to the goemetric path.

If this is incorrect, could you give a bit more detailed explanation.

thanks,

edz

I've measure the focal ratio of most binoculars at between 4.7 and 5.2 with a few down around 4.3 to 4.5. I've never seen any below 4.

### #6 Guest_**DONOTDELETE**_*

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Posted 02 March 2004 - 03:52 PM

Okay, my previous post was a bit short on details. Sorry about that.

Each prism can be thought of as a plane parellel glass block. As you mentioned, the entrance and exit faces are 90 deg to the optical axis. The light rays from the objective are converging when they hit the prism face and are bent. When they exit the prism face, they are once again bent. The net effect is that the prism block has displaced the image point further away from the objective by amount (N-1)*t/N, where N is the refactive index and t is the physical thickness of the prism block.

Since the focal length of the objective remain unchanged, the effective thickness of the prism block or "equivalent air thickness" is less than the actual prism thickness by this amount. So, the equivalent air thickness is t - (N-1)*t/N. This comes out to t/N.

So, if you are assuming the light rays go through the prism unaffected (not deviated by the prisms), then this equivalent air thickness is what needs to be used to estimate the focal length of the objectives. Alternatively, one can use the actual geometrical thickness of the prism but has to account for the shifting of the focal point as explained in the above paragraph.

All of this is explained in the text "Modern Optical Engineering" by Warren J. Smith, chapter 4.

### #7 EdZ

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Posted 02 March 2004 - 04:15 PM

Thanks for that much better explanation.

That being #2, Now you're off to a good start.

I'll use that, and I have an old post to modify to reflect that difference.

edz

### #8 EdZ

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Posted 02 March 2004 - 05:03 PM

I have a table of 16 different binoculars that is loaded with all the measurements to calc focal lengths. I modified the prism path length according to the above notes by dividing prism path/refractive index. Obviously it reduced the calculated focal length of all the models in my list.

What the table now shows

four models, 1 7x35, 2 8x42s and 1 10x50, have f#s of about 3.7 to 3.8
nine modesl have f#s from 4.0 to 4.3, most closer to 4.3
only the two models of 20x80s are slower, they have f# of 4.7 and 5.1

My BT100s (not in my list) are stated as f6.2 by the manufacturer.

edz

### #9 Guest_**DONOTDELETE**_*

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Posted 02 March 2004 - 05:56 PM

I have the understanding that because the light enters the prism face at exactly 90°, perpendicular to the glass surface, and exits the same way, the light is not bent. the refractive index of a medium would change the angle of the light as the light passed from one medium to another and if the light entered the medium at an angle other than 90°. It is bent at 90° when it hits the back of the prism, but in this case it has not yet exited the glass.

I've heard this quite a few times. It is true that the on-axis rays strike at 90 degrees, but the off-axis rays strike at an angle, the value of which increases with the distance off-axis. This presumably explains why false colour (CA) in binoculars tends to be zero on axis and increases towards the field edges.

One way to reduce this prism CA would presumably be to use low dispersion glass for the prisms, but this would be very expensive.

There is another way. One of the simplest eyepieces - is it the Huygenian? - uses 2 elements. The light rays between the two elements are parallel. So put the erecting prisms between the two eyepiece lenses, and they will introduce no CA. The binoculars might be a bit long though. Of course another advantage is that the bins would not have such a pronounced dog-leg shape and would thus be more like roof prism bins, and thus easier to hold for people with small hands.

### #10 Guest_**DONOTDELETE**_*

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Posted 02 March 2004 - 06:49 PM

This is very interesting. Thanks for the information everyone.

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