This is more of a physics question than electronics, but I figured I'd post to see if anyone knew anyway. The question concerns Fizeau's method of the speed of light using a wheel with various teeth. The formula is c = 2d/t where t = delta theta/ w; where c is the speed of light, d is the distance between the wheel and light source and t is time measured using the number of teeth and angular speed (w). The question I am trying to solve uses 720 teeth and asks for the minimal angular speed to correctly determine the speed of light to be 3 x10e8 at a distance of 11.45 km. I was wondering if the delta theta is 1/(2 * # of teeth) or it is always 1/720, cause my textbook seems to contradict itself in that sense and it is confusing me, also the internet has not been much help in the issue. Thanks
Possibly the source of confusion comes from the two definitions for t, or at least your explanations of t seem to be a bit different.
yes, a distance mirror. The thing is, a problem in my textbook (I will type it out now) uses 1/720 in the solution manual for 720 teeth. Here it is. (I get an answer which is one half the correct answer. The right answer is around 112 radian/sec I think) In an experiment to measure the speed of light using the apparatus of Fizeau, the distance between light source and mirror was 11.45km and the wheel had 720 notches. The experimentally determined value of c was 2.998e8 m/s. Find the minimum angular speed of the wheel for this experiment. What I did was; c = (2d)/t t=Theta/w t =[ (2*pi radians/2*720 (the 720 being the amount of notches) ] / w w = (2.998e8)(2*pi/1440) 2(11.45e3)
Light travels 11.45km to the mirror and another 11.45km back from the mirror. I could be wrong, but I always thought this is why "2" was in the divisor. I see you have it as "2(d)" as well as in the divisor. In other words, I would have solved with: w = (2.998e8)(2*pi/1440) / (11.45e3)