Problem 2 and 3

Here are more problems for us to have fun doing...


Problem 2:
It has been stated that Archimedes once saved the Greeks from attack by a Roman fleet by equipping a large number of well trained soldiers with large hand-held plane mirrors and getting them to reflect the sun's rays onto some part of a Roman ship at a distance of 100m, thereby setting it on fire. Comment on the feasibility of such a plan.  
You may assume that the mirrors are available, that the solar flux is 1 kW per meter squared, and that the angular diameter of the sun is 0.5 degrees. The ships may be assumed to be wooden. Stefan's constant is 5.7 x 10^(- 8) W m^(- 2)K^(- 4)


Problem 3: 
A parabolic mirror is made to focus the sun's disc into a circle of radius 1 cm. Estimate the smallest diameter of such a mirror if it can be used to melt iron. Make any assumptions that are plausible and necessary. Stefan's constant has been given with the above problem, the melting point of iron is 1535 degree celcius, the solar constant at the bottom of the atmosphere is 1 kW per meter squared.