Well, amazingly, the short answer is YES — but, it's all about the method.
A regular magnifying glass is able to set fire to a popcorn kernel quite easily. This however is not what we want. We need the moisture inside to boil, cook the starch and then burst the shell explosively.
We used a larger magnifying lens — a flat 'fresnel' book magnifier — and sat the kernels in some cooking oil in a teaspoon. I think the cooking oil is there just to spread the heat around the kernel rather any cunning cooking chemistry. After a while it will start bubbling (some of it's moisture boiling off) then after a while longer, if you're lucky, it'll explode. We managed to get a good few of them to pop but only one made a lovely big popcorn — the others were kinda half-hearted attempts at popping.
Focussing the sunlight too tightly on the kernel lead to burning. A loose focus on the teaspoon head spread the energy out to a more controllable level.
After all this discovery we went inside and hit the stove with a saucepan. They all popped in no time. It just goes to show how much energy your stove kicks out!
