MP8-1: Fringes from different interfering wavelengths (spoiler with explanation)

Hints for this problem: Start with the constructive interference equation, use the small angle approximation (sin x = x) and solve for theta when m=1 (it isn't m=0 because that would be for theta=0 and we know there is an nonzero angle based on the problem description).

The theta will be the same for the destructive scenario, since the destructive band with the second wavelength occurs in the same place as the constructive band for the original wavelength. Use m=0, since this is the first destructive interference band.

Solving this relationship shows you that the second wavelength is twice the first, which you then convert to micrometers.