Wicked kids scorch insects and light fires with a burning glass. This is just a simple magnifier capable of focusing and concentrating sunlight forming a hot tiny image of the sun. You should know, the camera lens is simply a more sophisticated, more corrected variety of the common magnifying glass. Actually if you dismount a camera lens and you have the predisposition, you can go about using it to burn and start fires.
Now your question revolves around the fact that telephoto lenses magnify thus they must perform this task giving superior results. Actually two optical factors intertwine making a burning glass. These intertwine in the camera and effect image brightness.
- The larger the working diameter (aperture opening) the greater the potential to project a bright, hot image of the sun. This is because a lens acts much like a funnel, the greater its working diameter, the more light energy it can gather and bring to a focus.
- The longer the focal length, the more the magnification. The greater the magnification the larger the projected image will be. Magnification spreads the image over a larger area. The result is a dimmer less energetic image.
- The fact that focal length and aperture are intertwined forces us to use a ratio to express the relative brightness of a lens. This is especially useful when we compare one lens to another. To express the light transmission ability of a lens, we divide the focal length by the diameter of the aperture. The result is called a focal ratio (f-number for short).
The f-number is the great leveler of the lens. If we set a lens to f/8, it will deliver the same brightness (heat in this case) as any other lens functioning at f/8, regardless --- regardless. In other words, set any lens to the same f-number, regardless of the other stuff, you get the same image brightness (same heat delivered), they are all equitable in this regard.