Burning wood with magnifying glass

[einai]

Hi,

In our class, we were asked whether it's practical to use a magnifying glass to focus sunlight to burn wood. One question really bothers me.

Could somebody please explain to me how the focal ratio (focal length of converging lens divided by its diameter) affects the temperature of the wood? It seems to me that only the collecting area (cross-sectional area) of the lens matters. I mean, no matter how long the focal length is, the light rays are still focused to the same point, right?

I know how to get the solar flux etc though. My only concern is the focal length.

Thanks in advance!

 

[kuba]

A very practical problem is that spherical lenses are rather imperfect. They, be definition, cannot focus a parallel set of rays (like from an "infinitely" distant sun) onto a point, unless their focal length is infinite.

So, the shorter the focal length of a lens is, the larger the area of the bright spot that is supposed to heat up the wood to ignite it.

Also, the lens' aperture matters here and no matter how perfect the lens'/mirror's geometry is, the aperture needs to be large if you want a single lens/mirror to do the job.

There are several ways to practically go about it:

1. Use a lens with longest practical focal length.

2a. Use an aspherical lens / aspherical mirror which could be made into "perfect" curvature needed to focus light into a point.

2b. Use a diffraction grating (say a fresnel lens) that can be flat, cheap and still work better than a short focal length lens.

3. Use a multi-lens system.

Real life example: when properly "fed" with sunlight via a collector/diffractor lens system, an objective from a miscroscope could make the spot's size comparable to the wavelength (about 1 micrometer - we're talking heat a.k.a. infrared here). That spot would be a very hot place indeed. You could possibly melt "kitchen" aluminum foil with that. I've tried it with a 150mm mirror (part of a telescope), a concave doublet as the diffractor, and a 50x Zeiss objective. On a sunny summer day it was a nice way to cut aluminum foil. Worked like charm, and burned your fingers too

Cheers, Kuba

 

[M98Ranger]

Hello,

Great question! The focal ratio does play a role in the temperature of the wood when using a magnifying glass to burn it. While the collecting area of the lens is important, the focal length also affects the concentration of light at the focal point.

Think of it this way, if you have a magnifying glass with a longer focal length, the light rays that pass through it will have a wider spread compared to a magnifying glass with a shorter focal length. This means that the light rays will not be as concentrated at the focal point, resulting in a lower temperature and potentially not enough heat to burn the wood.

On the other hand, a magnifying glass with a shorter focal length will have a narrower spread of light rays, resulting in a more concentrated beam at the focal point. This can generate a higher temperature and be more effective in burning the wood.

In short, the focal ratio is important because it determines the concentration of light at the focal point, which ultimately affects the temperature and ability to burn the wood. I hope this helps clarify your question. Let me know if you have any further questions.