So I've been doing some experiments, using bottles filled with various liquids and timing how long they take to burn paper which is placed at the focal point (where the light was focused). I've noticed that using denser liquids with high refractive indexes lower the focal length, and thus increase the lens power. This causes the bottle to be able to achieve a faster burn. Specifically, using glycerol in comparison to water in the same bottle allowed me to halve the time it took to achieve a burn. My question is, why? I've searched frantically over the net, and have found two answers I need explanation and elaboration on. 1. The inverse sq Law - this means that light being focused over a longer distance will diminish in intensity. However, I do not believe that this applies to this context. 2. A larger focal length means a larger focal spot, thus reducing intensity of the light - I simply don't understand this. Don't all convex lenses converge light onto one small spot? Why does the size of this spot change? Isn't this related to aberrations/refractive errors instead? Please, if possible include sources in your responses.