So infinitely many bands with finite intensity each would give an infinite intensity. Now, the formula for where the other peaks will be imply that for an infinitely long flat screen, you would have infinitely many bands of intensity equal to the one at the center. If you measure, say, the intensity of the main peak, you get a finite value.
Thank you for your reply! So I am aware that the energy is conserved, I am just not sure where does the formula for intensity breaks down. It is possible to show that the total power radiated over the # 4 \pi # steradians from two sources that make an interference pattern is equal to the sum of the individual powers. in spherical coordinates # I=I(\theta, \phi) #). # \\ # Energy is conserved for these interference patterns, but to show that, it is necessary to compute the pattern over the solid angle, (e.g. If # d > \lambda #, you get many, many closely spaced peaks, but this becomes an impractical case for interference. In the books and online resources that I read, this is given as: $$I = I_0 \cos^2(\frac #, where # m # is any integer. Hello! I am a bit confused by the formula for light intensity in the case of interference.
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