FYKOS Year 29 Series 2 Problem 5 — round it up · FYKOS 29 #29.2.5
Physics · optics
Problem
Mirek felt that during winter it is a little bit too dark for reading in his room. So he decided to make a hole in his wall for another window. He went to glass-works first to buy the glass panes. There was one nice round piece, but before he would buy it, he needed to check whether it's not too uneven (specifically convex). He placed the pane on the glass desk of the glass-works and saw rainbow circles around the centre of the pane caused by interference of the perpendicularly coming white light in the thin space between the two glasses. Mirek randomly chose two red circles (λ≈700nm) and measured with a ruler their diameters dk=(10,5±0,5)mm and dk+1=(13,0±0,5)mm. Based on these measurements he managed to determine the radius of curvature of the pane. Calculate it as well and think about it's errors.