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Field of View & Actual Magnification

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Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: August/11/2008 at 22:32
wamshane View Drop Down
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I am looking at Zeiss Conquest scopes.  I note that the field of view for the

3-9 x 40  is 11.01-33.9   while the field of view for the
3-9 x 50  is 12.9  -37.5  and the field of view for the

3.5-10 x 33 is  11.61-35.1  ....

... so is the field of view a more representative statement of the actual scope magnification range or perhaps the field of view is dependent on the objective size  or ????

... Is there a way to figure true magnification? 
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: August/12/2008 at 18:19
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Magnification is the ratio of the diameter of the objective lens to the diameter of the exit pupil.

Field of view is expressed in two ways: angular FOV and linear FOV.

For a conventional telescope, the angular field of view is the ratio of the apparent FOV of the eyepiece to the magnification. The apparent angular FOV of the eyepiece can be anywhere from 35 to 80 degrees, but a value of about 55 degrees is typical.

The variable ratio of 3-9 means there are lenses within the telescope that magnify the virtual image by a factor of three.

So, at a magnification of 9x, the angular FOV is approximately equal to (55/9)/3 = 2.037 degrees.

To convert this to linear FOV, remember that the ratio of the circumference of a circle to its diameter is a constant, 3.14159265.. At a distance of 100 yards (300 ft), the diameter of a circle is given by 2*3.14159265*300 = 1884.956 ft. Since there are 360 degrees in a circle, 1 degree is 1884.956/360 = 5.235988 ft. (as an aside, it is common for binoculars to express FOV at 1000 yards. In that case, the conversion factor is 52.359, which is generally rounded to 52.5)

2.037 degrees in angular FOV is about 10.67 ft for a linear FOV. Since FOV is inversely proportional to magnification, 3x will be 3 times larger or about 32 feet.

These are approximations, but show how FOV relates to magnification.

Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: August/14/2008 at 00:58
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Thank you very much for this detailed explanation and the examples.  Very helpful and my math degree/discipline did come into play to help.
 
Can you also say that if a lens has a larger objective...it will normally change the field of view...e.g. a 3-9x40 might have a smaller field of view than a 3-9x50 as there would be the impact of the diameter of the objective lens and the diameter of the exit pupil.
 
Thanks again for your help.  Now if I can just get the 6x6 or larger elk be in the field of view!
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: August/14/2008 at 06:48
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[QUOTE=wamshane] Can you also say that if a lens has a larger objective...it will normally change the field of view...[QUOTE]

No, I would not say that. It remains true that the FOV is determined by the ratio of the apparent FOV of the eyepiece to the magnification. To cover imperfections of one kind or another, aperatures can be placed within the scope to change the exit pupil, or to limit the effective diameter of the objective lens. The answer to your question comes from the definition of magnification.

I chose to describe magnification as the ratio of the diameter of the objective lens to the diameter of the exit pupil, because those are things you can measure and the explanation normally seen in these forums. In fact, magnification is more correctly the ratio of the focal length of the objective lens to the focal length of the ocular lens. Because the length of the scope remains the same, for all practical purposes, irrespective of whether a 40mm or a 50mm objective is used, the focal length of the lenses remains about the same for the 3x9,40 or 3x9,50. Hope this helps.
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: August/14/2008 at 08:55
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Great Explanation Tom and Welcome

Wes
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: August/14/2008 at 10:00
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GUNSOW75   TOM.....Your explanation was great THANK you for your imput......So easy to understand
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: August/14/2008 at 21:25
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Thank you again for the feedback and support.  I do believe I understand more than a bit better than before.  The Leupold catalog has much more specification data than the Zeiss catalog and actually lists actual magnification and some of the other data you mentioned.
 
Thanks again for the info ... and as mentioned before ... I just need to get the elk to appear in the field of view ! 
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: August/15/2008 at 04:38
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I have probably made it far too complicated. Just remember that actual FOV is apparent FOV divided by magnification. If we want to change it, we can only change the magnification or the apparent field of view. We can't change the actual magnification because that was a design choice. The angle of the light cone described by the outer edge of a lens and its focal point can be made larger if you shorten the focal length. For 9x, you set the focal length ratios for that mag. Of course, the scope can't be made 4 inches long for practical reasons. The only other variable that can be changed is the apparent FOV of the eyepiece. You have a 1 inch tube, or a 30 mm tube, which contains an even smaller tube, presenting the light to the eyepiece. There are always practical limitations to what can be done.
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: August/15/2008 at 07:06
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Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: August/15/2008 at 07:25
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Originally posted by Ed Connelly Ed Connelly wrote:

 
Ed, that is why you must sit in the front of the classroom, otherwise you nod off during important lessons.
 
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: August/15/2008 at 08:19
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Ed, you just made my day. (: ))

I will have a smile on my face for the rest of the day.

Now, it's back to work in good humor.
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: August/15/2008 at 09:08
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Originally posted by Ed Connelly Ed Connelly wrote:


I must say Ed, I have envisioned you a number of ways...never like that. The softer, gentler side of the Ringmaster of the Ed Show???
Post Options Post Options   Thanks (0) Thanks(0)     Back to Top Direct Link To This Post Posted: August/16/2008 at 14:27
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Originally posted by Gunshow75 Gunshow75 wrote:

[QUOTE=wamshane] Can you also say that if a lens has a larger objective...it will normally change the field of view...[QUOTE]

No, I would not say that. It remains true that the FOV is determined by the ratio of the apparent FOV of the eyepiece to the magnification. To cover imperfections of one kind or another, aperatures can be placed within the scope to change the exit pupil, or to limit the effective diameter of the objective lens. The answer to your question comes from the definition of magnification.

I chose to describe magnification as the ratio of the diameter of the objective lens to the diameter of the exit pupil, because those are things you can measure and the explanation normally seen in these forums. In fact, magnification is more correctly the ratio of the focal length of the objective lens to the focal length of the ocular lens. Because the length of the scope remains the same, for all practical purposes, irrespective of whether a 40mm or a 50mm objective is used, the focal length of the lenses remains about the same for the 3x9,40 or 3x9,50. Hope this helps.


Nice explanation.  As a general comment though, typically you will see scopes with larger objective lenses have slightly narrower field of view at the same magnification as scopes with smaller objective lenses.  If you keep the same focal length and use a larger objective lens, two things will happen: you will have harder time containing edge aberrations and your depth of focus will become shallower.  Most scope makers end up increasing the focal length a little when going to larger objectives in order to keep up with the optical quality.  If you are looking to get a fairly short scope with a large objective lens, get ready to pay a lot of money since the optics become quite a bit more complicated or the image quality will suffer.

ILya
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