Can any amount of water be heated enough to cause evaporation or possibly to boiling point by using a magnifying glass?
How big would a magnifying glass have to be in proportion to the amount of water?
If a glass container were used, would the water simply diffuse the effect of the lense or would a metal sphere do better?
To answer the first question you asked–
As a kid I used a cheap manifying glass(probably 5x or less) and caught a piece of paper on fire. That is 451F. Water boils at 212 F. so you COULD boil water. I’m not the one to tell you how MUCH water you could boil using a standard lens.
Well, let’s take a generously large 5" diameter magnifying glass. Give the approximate solar power density at the Earth’s surface is about 1.4 kW/m[sup]2[/sup], the lens, with an area of .0126 m[sup]2[/sup] can gather about 17.7 W of power. Assuming the container can absorb 100% of the incident light, that works out to 59 minutes to boil one cubic centimeter of water, assuming zero losses, if I’ve done my math right.
Hmmm…that seems long. Redoing calculations, I get 9.44 minutes, which sounds more correct to me. Anyone care to check me?
Q.E.D.:Your second number is in the same ballpark as what I get, although you’ve used a more optimistic solar constant than I have. (At Earth’s surface I think the values are more like 700-1000 W/m[sup]2[/sup]; the value of 1400 W/m[sup]2[/sup] is for just outside Earth’s atmosphere.)
Note that over a few minutes the water will probably transfer a lot of its heat to the container and the atmosphere, so I doubt if you could really boil 1 mL of water with a lens this small. But you could probably boil a droplet of water (~0.01mL) this way. You probably want to put the droplet on a dark heat-insulating surface (black garbage bag?) because water is pretty transparent.
Maybe I’ll try this next time I get out my Fresnel lens.
I left out a critical piece of information: The starting temperature I used was 20 [sup]o[/sup]C. And to save anyone who wants to double-check the trouble, it takes 1 calorie to raise the temperature of water 1 [sup]o[/sup]C and 1 watt = .24 calories/sec.
Now as the water heats it will start evaporation and that will remove that heat. You moght need a very large MG to actually get water boiling.
That said there are power plants that use mirrors to focus the sun’s energy to boilwater under pressure (higher temp then 212F).
I’m sure it is possible but could take somewhat longer the the 9.x minutes
What’s the reflective index (is that the right term?) of water? Certainly its not perfectly translucent; it must reflect some percentage of the incoming light back out.
The fraction of energy reflected when light is incident normally on an interface is [(n[sub]1[/sub] - n[sub]2[/sub])/(n[sub]1[/sub] + n[sub]2[/sub])][sup]2[/sup]. For an air-water interface n[sub]1[/sub] = 1.00 and n[sub]2[/sub] = 1.33, so about 2% of the energy is reflected.
Not to be a killjoy to all you calculating math types out there, but couldn’t any of you just have taken a lens and some water out to the porch and try the thing out?
Just as an aside here, it’s a lot easier to boil water with a 1920s-style death ray.
Was it Dogface who started this horror? If so is he aware of the absolute catastrophe he has visited on this board? Will it ever end? Or does all your base are belong to us?
It seems to me that on a clear day you’d be okay using the extra-atmospheric value to a good approximation. Does anyone know of a cite one way or the other?
Of course, for something flat on the ground, you’d multiply by the sine of the sun’s elevation, which could give you a value like 700-1000 for mid-latitudes. Is this what you had in mind?
It is alleged that Thomas Edison asked one of his employees to find the volume of a glass vessel, more specifically an ordinary light bulb.
the assistan/employee set about measuring and calculating, and sovering several sheets of paper with the operation
Edison’s approach was to simply fill the vessel with water and measure the volume in a standard graduated cylinder.
???
I don’t think I believe that cite, Q.E.D. All of the quotes in the cite seem to refer to the solar constant (about 1370 W/m[sup]2[/sup]), which is the value outside Earth’s atmosphere; it’s just the text below it that mentions the surface of the Earth. Here are some sites that talk about average absorption and reflection by atmosphere and clouds: Earth’s Radiation Budget and Solar Radiation. This site mentions values of 800-1100 W/m[sup]2[/sup] at the surface, but doesn’t provide any references or other info. I’ve seen that range mentioned before, and that’s what I was using, but I don’t know if that assumes a sunny day or not. I haven’t found any really authoritative answers though.
The two sites above give -8% to absorption and reflection by the atmosphere and another -23% by clouds, so maybe on a very sunny day you can get about 1200 W/m[sup]2[/sup]. I don’t know how much power gets reflected by different kinds of clouds, so I don’t know how likely “very sunny” days are.
You can buy a foot-square Fresnel lens from Edmund Scientific for about $5. Not only does it boil water, it melts solder. If you focus the noon sun on the side of small black-painted can of water, you can hear the water at the focus boiling almost immediately. It does take a while to bring all the water to a boil, of course.
Dammit, I was going to mention the Giant Fresnel Lenses!!! And how, when you buy the 4’x8’ size at EfstonScience in Toronto (affiliated with Edmund Scientific), you had to keep it covered when you took them across the parking lot or it’d melt the asphalt… 
I found a better reference for solar power density at the surface of the Earth. (It doesn’t seem to be online, though.) From the second edition of Physics Vade Mecum (published by AIP), §11.08A (Table: Intensity of Solar Radiation):
The actual table lists average intensities for several U.S. cities. Unsurprisingly, Seattle’s is lowest; El Paso has the highest year-round average (303 W/m[sup]2[/sup]).
As an aside, this is a truly excellent book for finding random physical constants. If anyone knows of an online version I’d love to know about it.
Now that sounds like a good way to spend the afternoon…melting a parking lot…
For what it’s worth, if anything:
A machined aluminum cup 1/2" OD x 29/64" ID x 1/2" high was blackened with ‘Magic Marker,’ filled with tap water, suspended between 1/32" sstl. wires over a mirror and a 5" magnifying glass oriented to focus the image of the sun on the bottom. Result: hot water.
Made cups from thin aluminum food wrap by coating dull side with Magic Marker, cut dime and quarter sized circles and formed cups, with the black inside, using a pencil and cap from a pen.
Nucleate boiling occured on the black surface in both cups but water mass remained just below boiling point. Regret lack of a micro thermocouple to measure temperatures.
Will have to get a Fresnel Lens!