# What equivalent laser power is required to simulate sun under magnifying glass?



## Variant (Mar 30, 2006)

Here's a techie/physics question that I’m sure involves some interesting formulas and math:

Approximately what power of laser would be equivalent to focusing the sun to a concentrated 2mm spot using a 3” diameter magnifying glass (assuming a clear sea level day with the sun basically straight overhead)?

Being the pyromaniac kid that I was at 8 years old, I remember burning lots of stuff with my magnifying glass. I remember that on a good summer day, I could create a fairly intense spot of sunlight with my magnifying glass that could ignite or melt virtually anything organic instantly…so I was just curious about what power of laser would be required to achieve similar “burning power.”

An explanation of how the answer is derived would be much appreciated (but not required--I welcome estimates and hunches to this answer).


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## AJ_Dual (Mar 30, 2006)

The solar constant of infalling sunlight is approximately 1337 Watts per square meter for the average of the entire Earth's surface. I don't know where you live Variant, but for argument's sake I'm going to assume you live in the U.S. at a temperate latitude. Giving you the benefit of the doubt, I'll say you were using your magnifying glass at noon near the Summer Solstice on a cloudless day. So I'll just accept the avereage solar constant. If you lived at the equator, it'll be higher, north pole, lower etc..

One Square Meter works out to about 1 550.003 square inches, or 1337W M^3/1550.003sqin. Or roughly 8.625 Watts/sqin.

The area formula for a circle is PiR^2 (3.14 X radius squared) so your 3" magnifying glass had an area of 3.14 X 1.5^2 = 7.065 sqin.

So 7.065 sqin X 8.625W/sqin is 60.936 Watts. That's about the thereoretical maximum of what your 3" magnifying glass was focusing down to a 1 or 2 mm point... 

Now, you can probably easily cut that figure in half, if not more, due to all the energy losses from the atmosphere, it not being the absoulte best day of the year for sun positioning etc, and the energy losses of frequencies like UV and IR that the glass lens wasn't passing. 

However, even a 20 or a 30 Watt laser is hugely powerful, relatively non-portable, and very expensive… There are some portable & semi-portable lasers in this range such as military rangefinders, but you won't find them on the market, and if you did, they would be even more expensive, also, they're not focused to burn stuff. Someone did post a video of a back-pack laser system for burning up gunk and paint, but I'm sure it was hideously expensive too.

Either way, it's nothing you'll achieve with a handheld pointer, even the thousand dollar+ units the size of a D-cell Maglite. The absolute best you'll achive with these is just under 1/2 Watt or 500 milliwats. Although these are more than capable of lighting matches, and cutting black plastic...

You could probably find a used CO2 industrial laser the range your magnifying glass put out for not too much money though. If you search the forum a few months back there was a video of a guy experimenting with a CO2 laser tube in about that range, burning stuff like paper and wood in his basment. (Very dangerous BTW, IR is not good for your eyes, it'll turn them white like a cooked egg, and unlike visible, you can't see it coming at you…)

I'm guessing an engineer or physycist would laugh to death at my math, but my gut tells me I'm in the ball park...  

So my final anser is that your magnifying glass had an actual output at it's focus of 20-30 Watts.


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## shawndoe (Mar 30, 2006)

AJ,


I question your math. You have 1337 Watts and 1550Sq/In so you should have something on the order of 1 Watt per Sq/in. That would mean that the Magnifying Glass will collect about 7 Watts of which you will lose between 2-4 Watts due to all the losses you mentioned. So in theory you would have the equivlent of between 3-5 watts in your spot. 

The effects of a magnifing glass are much closer to a 3 watt laser then a 20 Watt. A 30-40 Watt C02 will set light to wood a 3" magnifing glass won't even come close to that.

Have a good one.
Shawndoe


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## dr_lava (Mar 30, 2006)

I, too have wondered this, so I 'll take a shot at it. Starting with this:

http://en.wikipedia.org/wiki/Solar_power

The generally accepted standard is for peak power of 1020 W/m² at sea level.
because of wisconsin's latitude, this should be decreased to about 800W/m2.

The power hitting the lens of a 3 inch glass would be 3.6 Watts. Glass does block most IR wavelengths and the lens would not be able to focus the entire patch cleanly on 2mm, so I estimate a decrease in power from the input to output of the lens to be 50%. Thus, a 1.8 Watt laser should be roughly equivalent to an average SE wisconsonite magnifrying experience. 


How many kids do YOU think used goggles when burning things with a magnifying glass??????


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## LaserFreak (Mar 30, 2006)

Hehe...Magnifrying. I like that word!


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## winny (Mar 30, 2006)

AJ_Dual said:


> Someone did post a video of a back-pack laser system for burning up gunk and paint, but I'm sure it was hideously expensive too.



Interresting... Where?


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## comozo (Mar 30, 2006)

You could look at it this way.
So How Many Photons are Coming Out of My Laser?
This is a simple calculation based on knowing the energy of each photon (based on wavelength):

 1,240 nm
E = 1.602*10-19 J * -----------
lambda

Where:

* Lambda = wavelength of your light source.
* 1,240 nm = photon wavelength with an energy of 1 ev. 

Then, photon flux = P/E where P is the beam power.

For example, a 1 mW, 620 nm source will produce about:

1*10-3
------------------- = 3*1015 photons/second.
1.60210*10-19 * 2

Or you could look at it this way.
It is important to note that extremely high power densities are achieved at the focal point of a concentrated laser beam. A 10-milliwatt beam focused to a diffraction-limited spot 0.22 micrometers in diameter results in a power density of approximately 30-million watts per square centimeter. Such high energy levels can rapidly degrade or destroy lens and filter coatings, as... 
That's about 3000 watts per micron.
So you see it all depends which parameters are defined. You forgot to tell us what the focal length is for the magnifying lens.
http://www.repairfaq.org/sam/laserioi.htm#ioilpm4
http://www.olympusfluoview.com/theory/confocallaserintro.html


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## SuperNinja (Mar 31, 2006)

Side note:
I bought one of these: http://www.goldmine-elec-products.com/prodinfo.asp?number=G15756

It's powerful enough to set wood on fire in 5 seconds or less, and it can also make the surface of concrete explode (small explosions, with chips of concrete popping off)


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## AJ_Dual (Mar 31, 2006)

shawndoe said:


> AJ,
> 
> 
> I question your math. You have 1337 Watts and 1550Sq/In so you should have something on the order of 1 Watt per Sq/in. That would mean that the Magnifying Glass will collect about 7 Watts of which you will lose between 2-4 Watts due to all the losses you mentioned. So in theory you would have the Shawndoe


 
You're right on, I misplaced a decimal point when I divided the Watts/Sq in...



Oops. Yep, cut all my figures after that point down to 1/10th...

But a 3-4 Watt CW laser is still pretty "beefy"...


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## 2xTrinity (Jan 20, 2007)

> How many kids do YOU think used goggles when burning things with a magnifying glass??????


http://www-personal.umich.edu/~bclee/lens.html 

Here are some guys who used a 1 square meter fresnel lens to burn things, they had to buy welding glasses to tolerate the glare.


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## liveforphysics (Jan 20, 2007)

When I was in 6th grade, I bought the cracked lens from a 48" projection TV at a garage sale for $2. At the time, $2 was a pretty serious investment to me, and I actaully ended up breaking off the cracked corner of the lens before I actually got the thing home. Keep in mind, I was bringing it home via bicycle, and it was quite bulky.

Long story short, my dad took it away from me on the 2nd day of owning it after burning just about everything I could make it focus onto. I remember boiling asphault until it actaully started to offgas something that flamed. I remember writing my name in the lawn in a path of burned grass. I remember boiling water in a can, melting my shoes, charring the cover of my social studdies book, and no longer being able to see when I went indoors.

Those were the good days. Unfortunately it was that social studdies book cover that got my lens taken away... Hmmm... I wonder where dad put that lens...


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