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Thread: Lens calculation variables

  1. #1 Lens calculation variables 
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    I feel stupid for not being able to find this anywhere, so I will ask you guys. What is the variable that defines how small a lens will make a light beam's diameter? I know focal point is how far from the lens the light comes into focus, but what gives the diameter of the light at the focal point? I have a convex lens here that has a focal point of about an inch from the end of the surface, it also makes my monitor at a distance of 3 feet appear to be 1/2 the diameter of the lens at the focal point. If I wanted a lens of the same focal length that could make my monitor appear 1/10 the size of the lens diameter (1" btw), what variable would have to be changed?


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    Well, I have a theory as to why there isn't a variable to describe this. I think that when my convex lens forms the image at its focal point, all relevant light vectors ARE in fact single infinity small points (Ideally), but because of the way the light hit the lens, there is not one point, but trillions, hence forming a significant area of single points. This should mean then that if you were to have a concave lens of equal optical power at the convex lenses focal point, you would counter the convergence with equal divergence and create a continuously in focus image. This image could then be run through another convex lens and brought wholly to a single point. Is this at all correct? :?


    Of all the wonders in the universe, none is likely more fascinating and complicated than human nature.

    "Two things are infinite: the universe and human stupidity; and I'm not sure about the universe."

    "Great spirits have always found violent opposition from mediocrities. The latter cannot understand it when a man does not thoughtlessly submit to hereditary prejudices but honestly and courageously uses his intelligence"

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  4. #3 Re: Lens calculation variables 
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    Quote Originally Posted by Cold Fusion
    I feel stupid for not being able to find this anywhere, so I will ask you guys. What is the variable that defines how small a lens will make a light beam's diameter? I know focal point is how far from the lens the light comes into focus, but what gives the diameter of the light at the focal point? I have a convex lens here that has a focal point of about an inch from the end of the surface, it also makes my monitor at a distance of 3 feet appear to be 1/2 the diameter of the lens at the focal point. If I wanted a lens of the same focal length that could make my monitor appear 1/10 the size of the lens diameter (1" btw), what variable would have to be changed?
    You seem to be confusing two different things here, The diameter of the light at the focus and the magnification factor. The diameter of the light at the focus point is called the Airy disk, and is due to limitations caused by the diffraction of light. This has nothing to due with the size of the image, but instead determines the maximum resolution of the lens.

    The magnification for a single lens is found by:



    Where f is the focal length and do is the distance of the object from the lens.
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    This leads to my next question, how exactly does zoom and focus work inside a camera lens? I noticed that when I increase the zoom on my Nikon lens, the ENTIRE barrel (all of the optical elements) move forward about 3 inches at their limit. My impression of this was that the output of the last optical element is primarily divergent, so that when you move the entire lens forward, a smaller portion of the light actually hits the sensor since it has time to diverge more so by the time it reaches it, leaving more light to hit the walls of the camera than when it is not zoomed in; but then I noticed in my lenses optical diagram and many others, that the output should be CONVERGENT given the larger portion of convex lenses to concave lenses. I also did a test where I observed the path of the light coming out of the lens, and it also appeared convergent to me. So, why does it move the entire barrel forward if the above scenario is not its intention? Perhaps the true mechanism that provides the zoom is within the motion of the lenses amongst themselves, and the barrel moving is only a way to reposition the focal point to compensate for what you must inevitably be looking at differently or for what the mechanism did to the light?

    As for focus, form what I can tell turning the focus ring either reduces or increases the optical power/convergence rate of the final light output, hence repositioning the focal point? If so, how exactly do you modify optical power without entirely introducing a new lens to the system to attenuate the power of the other lenses? I have stared at my lens's diagram for hours on end and just cannot figure it out.
    Of all the wonders in the universe, none is likely more fascinating and complicated than human nature.

    "Two things are infinite: the universe and human stupidity; and I'm not sure about the universe."

    "Great spirits have always found violent opposition from mediocrities. The latter cannot understand it when a man does not thoughtlessly submit to hereditary prejudices but honestly and courageously uses his intelligence"

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    Quote Originally Posted by Cold Fusion
    This leads to my next question, how exactly does zoom and focus work inside a camera lens? I noticed that when I increase the zoom on my Nikon lens, the ENTIRE barrel (all of the optical elements) move forward about 3 inches at their limit.
    Not all of the optical element move. Zoom works by moving some elements relative to others in order to change the effective focal length. Try searching wiki for "Zoom lens".
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    The world really makes it hard to learn this stuff, doesn't it? That article described a physically impossible way to zoom the image...its only when you reconsider what parts of the image are and add a component that it makes sense. They showed all of the light focusing on the CCD (or w/e else) no matter what. If so, then how can it zoom? Zoom is based off of only a portion of the light hitting the sensor. You have to add either a limiter or make the final focusing lens smaller in order to 'zoom'. This simplified version causes more problems than it creates, luckily it sparked my imagination to reconfigure my hypothesis and form an agreeable one finally.

    I wish the scientific community would stop simplifying things....I would rather take a very difficult but REAL problem head on then easily solve a simplified problem that does not work in reality. The Relativity wizards on this forum almost caused my head to explode with their explanations, BUT I AM GRATEFUL FOR THAT BECAUSE IT WAS THE REAL DATA, NOT SOME DELUSIONAL CRAP. And because of that I now have a very very good understanding of relativity.
    Of all the wonders in the universe, none is likely more fascinating and complicated than human nature.

    "Two things are infinite: the universe and human stupidity; and I'm not sure about the universe."

    "Great spirits have always found violent opposition from mediocrities. The latter cannot understand it when a man does not thoughtlessly submit to hereditary prejudices but honestly and courageously uses his intelligence"

    -Einstein

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    Quote Originally Posted by Cold Fusion

    I wish the scientific community would stop simplifying things....I would rather take a very difficult but REAL problem head on then easily solve a simplified problem that does not work in reality. The Relativity wizards on this forum almost caused my head to explode with their explanations, BUT I AM GRATEFUL FOR THAT BECAUSE IT WAS THE REAL DATA, NOT SOME DELUSIONAL CRAP. And because of that I now have a very very good understanding of relativity.
    Yes.

    You need to be careful about internet sources. Wiki is usually very good, and it is a definite asset for learning many subjects.

    But not all.

    There seem to be some fairly well organized groups of nut cases that exist on the internet and sometimes they infect Wiki, which is not a controlled source. I get the impression that sometimes the work of very competent people on Wiki articles is slightly twisted by people with an axe to grind, and the result is that not all Wiki articles are reliable.

    I think the problem is particularly pronounced with regard to topics that are of interest to the people who advocate the "electric universe", which means topics involving plasma physics in particular. You need to read those articles with a skeptical eye and ignore the tenets of the EU crowd. Fortunately as they abhor mathematics and are totally inept at all things mathematical they generally don't mess up that part.

    One source that is almost always good are classic texts. You won't go wrong by reading recognized texts written by real scientists and mathematicians. Avoid the books written by the lunatic fringe and stick to books that are widely recognized as "the best" and you won't go wrong. There are no conspiracies in mainstream science and mathematics.

    Beware of popularizations. Some are very good. Some seem to push an agenda, and present speculative and conjectural material as though it was known to be true. I find this particularly the case with topics involving "string theory". I am not saying that string theory is wrong. I am saying that string theory is still not proved and that conclusions regarding physics that come from string theory are conjectural at best. String theory has yet to produce a significant physically testable prediction.

    The mathematics that arises from string theory is a different matter. It has generated some profound and very deep mathematics. Mathematics relies on proof via logic which is therefore verifiable. But there is a lot of hand-waving done with regard to the mathematical manipulations that purport to describe physics within string theory, and that remains to be shown to be correct. It would be a big step forward, for instance, if the string theorists could give a rigorous definition of what string theory actually is.

    String theory may yet grow up and prove to be a huge step forward. But it has not reached that stage yet. You do not get that impression from the popularizations and in fact they seem to give the opposite impression. Be skeptical when you read them.

    If you want recommendations on good texts, the real thing, for a specific subject, just ask. I am sure that someone on the forum can make a good suggestion.
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    Beware of popularizations. Some are very good. Some seem to push an agenda, and present speculative and conjectural material as though it was known to be true.
    I have noticed this everywhere, particularly in topics pertaining to the creation of the universe. I really hate it when some guy comes on and says, "There were exactly 400,000 particles called bannanacreampies precisely .000047832 seconds after the universe was born". I even just watched a show on the History Channel where some guy claimed he knew EXACTLY what the inside of the event horizon looks like, and was audacious enough to render a meticulous CAD animation of its appearance. I feel that these people make such ridiculous claims in order to garner funding and support from the uneducated who do not know any better.

    I have decided to forgo the doctrines of optics and took a purely geometrical approach to it. From my thought experiments I found that at the focal point of a convex lens, if you were to place either a convex or concave lens of the correct optical power you would be able to maintain the focus infinitely (ideally) while either diverging or converging the light beams total diameter. It appears as if you cannot have a continuous focal point that is neither converging or diverging right at the first focal point in the optical system; however, once you have the continuous focus diverging/converging beam you could place an appropriate lens of equal optical power to correct for movement and for a straight continuous focus beam. Is this possible? I am not sure how to run through the calculations for this so I am not sure how to confirm it.
    Of all the wonders in the universe, none is likely more fascinating and complicated than human nature.

    "Two things are infinite: the universe and human stupidity; and I'm not sure about the universe."

    "Great spirits have always found violent opposition from mediocrities. The latter cannot understand it when a man does not thoughtlessly submit to hereditary prejudices but honestly and courageously uses his intelligence"

    -Einstein

    http://boinc.berkeley.edu/download.php

    Use your computing strength for science!
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  10. #9  
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    Quote Originally Posted by Cold Fusion

    I have decided to forgo the doctrines of optics and took a purely geometrical approach to it. From my thought experiments I found that at the focal point of a convex lens, if you were to place either a convex or concave lens of the correct optical power you would be able to maintain the focus infinitely (ideally) while either diverging or converging the light beams total diameter. It appears as if you cannot have a continuous focal point that is neither converging or diverging right at the first focal point in the optical system; however, once you have the continuous focus diverging/converging beam you could place an appropriate lens of equal optical power to correct for movement and for a straight continuous focus beam. Is this possible? I am not sure how to run through the calculations for this so I am not sure how to confirm it.
    Your description is a bit imprecise so it is hard to answer precisely.

    But if I understand what you are saying the anser is "no".

    I think you could do what you say IF the initial light source provided perfectly parallel light rays. But no source at a finite distance from the lens actuall does that.

    You see this effect as a practical matter when you consider the action of a single lens. Theoretically, given parallel light rays, a lens will focus them to a point at a distance equal to the focal length from the lens. So, if the sun provided perfectly parallel light rays, a magnifying glass would, at the focal lenth, focus those rays to a point and provide a point of infinite temperature, or slightly defocused, but to an arbitrarily small disc, a disc of arbitrarily high temperature.

    But thermodynamics show that such is not possible, as it would permit heat transfer from a colder source to a hotter sink. The resolution is that the rays of the sun are not perfectly parallel, and the lens cannot focus to an arbitrarily small disc, but in fact there is a limit, an image size for the image of the sun. That limits the temperature of the spot to the surface temperature of the sun.

    So, you can do what you are describing in terms of geometrical optics with the usual idealizations. But to have the actually light ray configuration that you describe you need a source that provides a perfect plane wave, and that you will not actually find. There will be divergences and aberations.
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    Quote Originally Posted by DrRocket
    So, if the sun provided perfectly parallel light rays, a magnifying glass would, at the focal lenth, focus those rays to a point ant
    Hey, I used to do that when I was a kid.
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    Quote Originally Posted by Harold14370
    Quote Originally Posted by DrRocket
    So, if the sun provided perfectly parallel light rays, a magnifying glass would, at the focal lenth, focus those rays to a point ant
    Hey, I used to do that when I was a kid.
    Thanks. Typo fixed.

    That was proabably hard on the ants, if you could track then with the focal point.
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    Is there any known way to create perfectly parallel light beams (non laser)?
    Of all the wonders in the universe, none is likely more fascinating and complicated than human nature.

    "Two things are infinite: the universe and human stupidity; and I'm not sure about the universe."

    "Great spirits have always found violent opposition from mediocrities. The latter cannot understand it when a man does not thoughtlessly submit to hereditary prejudices but honestly and courageously uses his intelligence"

    -Einstein

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    Use your computing strength for science!
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  14. #13  
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    Quote Originally Posted by Cold Fusion
    Is there any known way to create perfectly parallel light beams (non laser)?
    No. And that includes lasers. Lasers have dispersion just like other sources. That is why laser spot sizes increase with distance.

    In theory you could do it with a perfect point source located precisely at the focus of a perfect parabolic reflector. But the required perfection is not achievable.
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