How to heat water using a magnifying glass? If I want to heat a mug of water using a magnifying glass or glasses, how to I work out the size of glass needed, how many are needed to do the task in a set time?
 A: The magnifying glass only bundles the solar radiation and energy flux to a smaller cross section. Thus a magnifying glass can only then be advantageous for the heating of your mug in the sun when its area is substantially larger than the cross section of your mug. Otherwise direct solar heating should be better. You should keep also in mind that there is a loss of light transmission through the glass due to reflection and absorption.
A: As Cursed has pointed out in the comments, water is transparent, so it doesn't really work out that way.  On the other hand, you could try aiming the magnifying glass at the inner surface of the mug to allow the water to gain heat via conduction and convection.
As to how to speed up the heating, a larger magnifying glass would work better.  The equation is given by $$r_{image}=\frac{r_{sun}}{d_{sun}}f$$
Where $r_{image}$ is the radius of the image of the sun formed, and $r_{sun}$ is the radius of the sun, $695700$km.  $d_{sum}$ is the distance to the sun, $149600000$km and $f$ the focal length.  Hence $\frac{r_{sun}}{d_{sun}}$ is about $4.6\times 10^{-3}$.  In addition, the intensity of the sunlight is around $1kWm^{-2}$.  From here you can probably work it out.
A: A portable solar heater for a mug would use either a Fresnel lens or a concave reflector instead of a magnifying glass.
Ideally, it would be foldable and very lightweight. The optical quality does not need to be very good since a mug is fairly large.
Probably something like a spring wire loop holding a half-aluminized Mylar balloon would do the trick:

