I am doing an experiment which involves starting a fire with a magnifying glass. I need help in coming up with what variable I should vary. So far I have come up with absorptivity of the material, light source, the color of the light source, and also the environmental factors (humidity, altitude, oxygen levels etc.). What are some other possible variables for the burning glass experiment?

Distance at which photons passing through glass will focus is one of the most important variables..

 

https://en.wikipedia.org/wiki/Focal_length

 

Ok... but I need less obvious variables. For example, maybe something to do with the absorption spectra of the material?

You could consider various types of white paper which can't be directly burnt with your glass, only charred. You could brown but not overly oxidise a sufficient area that you can then take advantage of increased absorption to ignite the paper. Some skill required, at least for an eight year old, IIRC.