# Constructing a homemade magnifying glass that has a 100-foot focal point **URL:** \ **Category:** Factual Questions\ **Created:** [September 4, 2024, 1:19am UTC](https://boards.straightdope.com/t/constructing-a-homemade-magnifying-glass-that-has-a-100-foot-focal-point/1006709 "2024-09-04T01:19:50Z")\ **Posts on this page:** 11\ **Page:** 3
**Author:** ![md-2000](https://avatars.discourse-cdn.com/v4/letter/m/9d8465/32.png) [@md-2000](https://boards.straightdope.com/u/md-2000)\ **Post date:** [September 10, 2024, 3:52am UTC](https://boards.straightdope.com/t/constructing-a-homemade-magnifying-glass-that-has-a-100-foot-focal-point/1006709/41 "2024-09-10T03:52:34Z")
> [@Francis\_Vaughan](#): > > The example is assuming a stationary sun. It is trying to provide an explanation about why you can’t focus an extended source - such as the sun - onto an arbitrary point. The system always ends up creating an image of the extended source the size of which is defined by the focal length of the optics and the angular extent of the source. Exactly. People build telescopes (mirror or lenses) with longer focal length to get bigger images so they can see more detail in the celestial objects. Then they have to make the diameter bigger to capture enough light to see that detail without a very long exposure. Do this thought experiment. Draw a point A which epresents one spot on your magic lense or mirror. From A, draw a line to the center of the sun S. then draw 2 lines to the edge of the sun’s discS1 and S2. (The disc is ½° so there will be one line with two others, one on each side spreading ¼° from that centerline AS. Those lines reflect or refract at an angle to target T 100’ away. Since the mirror or lens does what they are supposed to do, each line changes direction the same amount. So now draw lines AT to target, and the lines from the edge of the suns disc will also be ¼° from AT at AT1 and AT2 The same applies to every spot on the lens (or mirror) they all aim at the same point T. 100 feet at ¼° is 0.44 feet or 5.24" so draw a circle radius 5.24" (diameter 10.5") around T and _that is the smallest image of the sun you can get with a 100 foot focal length mirror or lens._ When you are frying ants or burning paper, you are taking a 3" or so glass and concentrating all that solar energy into a spot a tiny fraction of an inch diameter. Let’s say your paper fire starter lens is focal length 6" so produces about 1/20" spot. Ratio of 3:0.05 or 60:1 concentration. For the same effect at 100 feet you would need a lense or mirror 60x10.5" = 630" or 52’ 6" diameter. ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [September 10, 2024, 12:12pm UTC](https://boards.straightdope.com/t/constructing-a-homemade-magnifying-glass-that-has-a-100-foot-focal-point/1006709/42 "2024-09-10T12:12:37Z")
> [@md-2000](#): > > Exactly. People build telescopes (mirror or lenses) with longer focal length to get bigger images so they can see more detail in the celestial objects. Actually, the reason that early telescopes had long focal lengths was because they hadn’t yet learned enough about figuring a mirror to properly parabolize it and get rid of spherical aberration. The longer the focal length, the closer the shape isd to a parabola and the smaller the error. They also had problems with chromatic aberration that were minimized with lng focal length mirrors: > [@](#): > > The [sharpness](https://en.wikipedia.org/wiki/Sharpness_(visual)) of the image in Kepler’s telescope was limited by the [chromatic aberration](https://en.wikipedia.org/wiki/Chromatic_aberration) introduced by the non-uniform refractive properties of the objective lens. The only way to overcome this limitation at high magnifying powers was to create objectives with very long focal lengths. [Giovanni Cassini] in 1672 with a telescope 35 feet (11 m) long. Astronomers such as [Johannes Hevelius] were constructing telescopes with focal lengths as long as 150 feet (46 m). Besides having really long tubes these telescopes needed scaffolding or long masts and cranes to hold them up. Their value as research tools was minimal since the telescope’s frame “tube” flexed and vibrated in the slightest breeze and sometimes collapsed altogether. > **[History of the telescope](https://en.wikipedia.org/wiki/History_of_the_telescope)** > > The history of the telescope can be traced to before the invention of the earliest known telescope, which appeared in 1608 in the Netherlands, when a patent was submitted by Hans Lippershey, an eyeglass maker. Although Lippershey did not receive his patent, news of the invention soon spread across Europe. The design of these early refracting telescopes consisted of a convex objective lens and a concave eyepiece. Galileo improved on this design the following year and applied it to astronomy. I... ---
**Author:** ![JacobSwan](https://avatars.discourse-cdn.com/v4/letter/j/a6a055/32.png) [@JacobSwan](https://boards.straightdope.com/u/JacobSwan)\ **Post date:** [September 10, 2024, 12:43pm UTC](https://boards.straightdope.com/t/constructing-a-homemade-magnifying-glass-that-has-a-100-foot-focal-point/1006709/43 "2024-09-10T12:43:51Z")
> [@Cartooniverse](#): > > He had someone craft a very large very thin metallic mirror. It spans about 5 ft across. It is a circle and it is mounted into a vacuum pump back. One of my uni professors had a small amount of NASA funding to investigate vacuum pump backed mirrors for space telescopes. They would have allowed changes to the focal length and corrections to any manufacturing defects. He got a lot of schadenfreude from his work not being included on Hubble. ---
**Author:** ![beowulff](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/beowulff/32/542_2.png) [@beowulff](https://boards.straightdope.com/u/beowulff)\ **Post date:** [September 10, 2024, 1:49pm UTC](https://boards.straightdope.com/t/constructing-a-homemade-magnifying-glass-that-has-a-100-foot-focal-point/1006709/44 "2024-09-10T13:49:48Z")
Well, to be fair - it’s kind of hard to use a vacuum pump in a vacuum. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 10, 2024, 9:35pm UTC](https://boards.straightdope.com/t/constructing-a-homemade-magnifying-glass-that-has-a-100-foot-focal-point/1006709/45 "2024-09-10T21:35:55Z")
That might have been the dominant reason for early telescopes, but even modern astronomical telescopes usually have fairly long focal lengths, because resolution is usually something that’s desired. ---
**Author:** ![Cartooniverse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cartooniverse/32/3084_2.png) [@Cartooniverse](https://boards.straightdope.com/u/Cartooniverse)\ **Post date:** [September 11, 2024, 12:38am UTC](https://boards.straightdope.com/t/constructing-a-homemade-magnifying-glass-that-has-a-100-foot-focal-point/1006709/46 "2024-09-11T00:38:28Z")
🤣 What a gift you are. > [@beowulff](#): > > Well, to be fair - it’s kind of hard to use a vacuum pump in a vacuum. ---
**Author:** ![Xocomil](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/xocomil/32/14927_2.png) [@Xocomil](https://boards.straightdope.com/u/Xocomil)\ **Post date:** [September 11, 2024, 1:30am UTC](https://boards.straightdope.com/t/constructing-a-homemade-magnifying-glass-that-has-a-100-foot-focal-point/1006709/47 "2024-09-11T01:30:48Z")
I hope I didn’t come across too harshly, I agree that the Mythbusters were too hasty in their dismissal. The fact that someone was able to set tarred hemp on fire made me think of one use of this method. Simply send out a highly combustible raft and set it ablaze from a distance and inspire awed terror. On the other hand, I have to imagine that even back then everyone was familiar with the concept of reflecting sunlight off a shiny surface so maybe terror but not awe. But if you were in range of that weapon you may soon be in range of the [Claw of Archimedes](https://en.wikipedia.org/wiki/Claw_of_Archimedes) which I gotta say scares me 2000 years later. Clever chap, that Archimedes. ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [September 11, 2024, 9:11am UTC](https://boards.straightdope.com/t/constructing-a-homemade-magnifying-glass-that-has-a-100-foot-focal-point/1006709/48 "2024-09-11T09:11:37Z")
> [@Chronos](#): > > That might have been the dominant reason for early telescopes, but even modern astronomical telescopes usually have fairly long focal lengths, because resolution is usually something that’s desired. But resolution doesn’t require long focal length. Resolution requires a large aperture. The Hubble and other space telescopes are necessarily a lot smaller than those early scaffold-mounted telescopes partly because they have to be launched in a vehicle, but if they _had_ to be long they could be assembled in orbit (with, I admit, quite a bit of difficulty). They haven’t been, because it’s not needed. But all of them have large apertures. Of course, it becomes difficult to have low aberration with a short focal length yet large aperture telescope, but it’s doable. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 11, 2024, 10:45am UTC](https://boards.straightdope.com/t/constructing-a-homemade-magnifying-glass-that-has-a-100-foot-focal-point/1006709/49 "2024-09-11T10:45:21Z")
Focal length still helps. If nothing else, eventually you run up against the physical size of the pixels (or equivalent) on your sensor. It does you no good to have an optically-sharp image at your sensor, if that image is itself too small to fully resolve. Granted, we can make some mighty small sensors these days (driven largely by the phone market), but this would have been an issue for, for instance, the Hubble. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [September 11, 2024, 3:05pm UTC](https://boards.straightdope.com/t/constructing-a-homemade-magnifying-glass-that-has-a-100-foot-focal-point/1006709/50 "2024-09-11T15:05:57Z")
Spy satellites use folded optics to achieve very long focal lengths. This is practical because they’re imaging the Earth’s brightly sunlit surface as opposed to a dim astronomical object. As a result they can blow up an extraordinarily tiny angular view to the limits of the resolution of the primary. ---
**Author:** ![Caribbean\_cruiser](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/caribbean_cruiser/32/9349_2.png) [@Caribbean\_cruiser](https://boards.straightdope.com/u/Caribbean_cruiser)\ **Post date:** [September 13, 2024, 7:50pm UTC](https://boards.straightdope.com/t/constructing-a-homemade-magnifying-glass-that-has-a-100-foot-focal-point/1006709/51 "2024-09-13T19:50:20Z")
> [@Dewey\_Finn](#): > > I gotta ask; why do you _need_ a magnifying glass with a 100-foot focal length? Are you preparing for a real-life _[Them!](https://en.wikipedia.org/wiki/Them!)_ (1954 monster movie with giant ants) situation? Purely a thought experiment. 😉 [Previous page](https://boards.straightdope.com/t/constructing-a-homemade-magnifying-glass-that-has-a-100-foot-focal-point/1006709.md?page=2)