Can you boil/decontaminate water with heat from a magnifying glass?
A bit hypothetical, but ruling out being able to use a solar still, or the SODIS method, could you make water drinkable by using the suns heat through a magnifying glass?
Paper self ignites at 451° F , water boils at 212° F, but that is at one concentrated point when paper burns using a magnifying glass. Would it be possible to boil a small about of water using the same method? For sake of it lets say you have a magnifying glass that is 3.5" across, and a plethora of different small containers available glass or metal.
I realize you could then start a fire, and boil water in a metal container but i am just curious if it is possible to heat the water enough to be drinkable without placing it on a fire using this method. As fires cause smoke lets say you are in a less than desirable place where the smoke from a fire could give away your location when you didn't want it to.
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Maybe you could have a very thin glass tube attached to a bigger will of water a bit like a watering can but with a thin spout then use a magnifying glass to boil water in the very top of the tube and condense the steam The well of water would top the tube up So all the time you are boiling a teaspoon ish amount of water I have seen how instantly a magnifying glass can burn my skin Just an idea to stop having to heat up all the water in one go
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Let's do some back-of-the-envelope calculations.
The specific heat of water is the amount of energy needed to raise the temperature of a particular amount of water by 1 degree C. This is 4.186 joules/gram °C (reference).
To raise the temperature of 1 L of water (1000 g) by 80 degrees C (to boiling from room temperature), would be 4.186 * 1000 * 80 = 334,800 joules.
The amount of sunlight falling on a square metre of the earth's surface is at maximum about 300 watts/m² (reference). A watt is a joule per second, so this means you could get 334,800 joules from a square metre of sunlight in 334,800 / 300 = 1116 seconds, or about 19 minutes.
Of course, a magnifying glass with an area of a square metre would be rather heavy and unwieldy to carry. A largeish one of 9 cm (3.54 inch) diameter would be about 64 cm², or 0.0064 square metres. Using this magnifying glass would boil our 1 litre of water in about 157 times as much time, or about 175,000 seconds, or just over 48 hours.
As you can see, the amount of energy you can collect directly from the sun is insufficient to boil any useful amount of water in a reasonable time. Even if you only wanted a small drink of 100 mL, it would still take all afternoon.
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The discussion is indeed theoretical because it seems impractical - however possible - to me. First of all, there is a big difference between paper (solid) and water (liquid). In the liquid, the absorbed light energy is distributed by molecular movement rather quickly and you will not necessarily get such a hot spot as on a piece of paper. The fraction of absorbed light will of course anyway heat the water.
Also, there is a difference if you use a magnifying glass or a mirror. A magnifying glass works in transmission without changing the mean direction of the light much. Therefore, it will only shine significantly more light onto the water - and with this cause an additional overall heating effect - if its surface is bigger than the projection of the container surface into the direction of the incoming light. A mirror is different indepentent of its size because it works in reflectance an can redirect a lot of light onto the water which would not have hit the water otherwise.
However, as paparazzo already indicated in a comment, water is transparent in the UV and most of the visible spectrum, so a big part of the solar energy is not absorbed by water at all. This source claims that 50% of the solar light energy is infrared light which is readily absorbed by water. They say that almost all infrared light is absorbed within the first 10 cm, so your container would have to be that deep for maximum energy absorption, and with this maximum heating rate, caused by light absorption of water. As we can safely assume that we are in the domain of linear optics, absorption follows Beer´s Law which states that light intensity drops exponentially with penetration depth, so having a little less than 10 cm container depth is probably not a big deal.
What is equally important like light absorption by water is light absorption by the container. If you have a black pot it will additionally absorb most of the visible (and probably UV) solar light and this will then heat up your water much quicker. This is also how solar showers (note that they do not use any focussing optics), cookers etc. work. Appropriate estimations of heating rates under such full absorption scenarios are already given in the answer by Greg Hewgill and corresponding comments.
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