[Optics] Starting a fire with a magnifying glass

[Atrika]

Hi, I'd like to know what makes a http://tinyurl.com/4dp9ocl" better at starting a fires by focusing the sun light. Is it the magnifying power, it's size, it's thickness (etc.) ? Also, is there a formula to calculate it ?

Thank you.

-Philippe

 

[tiny-tim]

Welcome to PF!

Hi Philippe! Welcome to PF!

It's really only the size …

the total heat output equals (obviously!) the heat input, which is proportional to the area of the lens.

(the magnifying power only alters the position of the focus, not the amount of heat there)

 

[Atrika]

Hi Philippe! Welcome to PF!

It's really only the size …

the total heat output equals (obviously!) the heat input, which is proportional to the area of the lens.

(the magnifying power only alters the position of the focus, not the amount of heat there)

Hi Tim, isn't it also affected by the magnifying glass' ability to pinpoint light?

ex: I have a 2" magnifying glass that produces an image of the sun of 2mm
I have a 4" magnifying glass that produces an image of the sun of 4mm

Both images will have the same heat output/size so the 4" magnifying glass won't start a fire faster, am I right ?

edit:
"As you said, spot size will be determined in part by lens aberrations. You can get rid of chromatic aberrations by using a fancy compound lens, or more simply by using a parabolic mirror instead. If you get rid of all aberrations, then the spot size will be the focal length times the angular size of the sun in the sky (9.6 milliradians)." -Krab

Does this mean that the most important factors are the size and the quality of the lens ?

 

[Andrew Mason]

Interesting question. Tim's point about the area of the lens determining the amount of energy that can be gathered to a spot must be correct. But whether that will make the spot any hotter (higher temperature) than a lens with a smaller area is a slightly different issue. To make it as hot as possible you would have to have the image of the sun as small as possible, which is a matter of having as short a focal length as possible. So it would seem to me that having the largest ratio of lens area to image area (or focal length) would give you the highest temperature.

Whether that will start a fire faster, though, may depend on what it is you are trying to light. A small spot at a high temperature might not be as good as a large spot at a lower temperature (but still higher than the ignition temperature of what it is you are trying to light).

AM

 

[Atrika]

Interesting.

 

[Gordianus]

Disregarding spherical aberrations, the f# of the lens is the key figure. In the geometrical limit, a large f# lens collects lots of energy and focuses it in a small spot.
My Swiss Army knife has a a magnifying glass whose f# is about 1 (2 cm diameter and 2 cm focal length). It performs very well as a fire igniter (dry leaves, small twigs)

 

[Andy Resnick]

This was first worked out in connection with searchlights- how powerfula light must be to illuminate a target- and is presented very nicely by Slyusarev, in "On the Possible and Impossible in Optics" (FTD-TT-62-175-1+2).

Using the sun as a source (subtending 31' of arc), the formula simplifies to

E = E0 (110/F)^2,

where E is the irradiance (W/m^2, for example) using a lens with a certain f-number (F, F = focal length/diameter), and E0 is the irradiance from the sun (1 kW/m^2 at most). For example, using a lens at f/2 increases the irradiance by 3000, and can easily set fire to small bits of wood.

Whether or not you can set fire to something requires a balance between incident power and power radiated by the hot object; this balance shows that the 'bare' sun cannot heat a body beyond 120 C. Dry wood ignites around 600C, in order to ignite wood within 30 minutes requires incident power approximately 40 times the 'bare' sun; to ignite wood within 8 seconds requires 100 times the incident power.

 

[Atrika]

If F = focal length / diameter, it means both are equally important.
Is there a way to find out the focal length of a magnifying glass before buying it ? The only thing written on the boxes is the magnification and the diameter of the lens.

 

[Nik_2213]

I used to have a double-element lens salvaged from broken binoculars which was a remarkably effective fire-starter: Thanks to the doublet, the chromatic abberation was very small, multiplying the effective size of the lens...

 

[Andy Resnick]

If F = focal length / diameter, it means both are equally important.
Is there a way to find out the focal length of a magnifying glass before buying it ? The only thing written on the boxes is the magnification and the diameter of the lens.

The focal length of a lens is not related to the magnification. Most magnifying lenses have fairly short focal lengths- much less than a meter, usually several centimeters or less.

 

[Atrika]

The focal length of a lens is not related to the magnification. Most magnifying lenses have fairly short focal lengths- much less than a meter, usually several centimeters or less.

Yes, I see. Thank you all for your help.