Question

With a Michelson interferometer, how much can the lengths of the alternative paths vary and still result in interference? For example, could one path be twice as long as the other?

Answer 1

Provided the waves vary by an integer multiple of their wavelength, then then constructively interfere with each other.

For instance, the wave sin(x) has wave length \( 2 \pi \). A wave of the form sin(x + 2.pi) interfers constructively with sin x giving
\[ \sin x + \sin(x + 2\pi) = \sin x + \sin x = 2 \sin x \]
Notice that for any integer multiple of 2pi we get positive interference because
\[ \sin(x + 2k\pi) = \sin x \ \ \ \ \hbox{ for all integers } k \]

Answer 2

Similarly, if the difference between the two waves is half a wavelength, or half a wavelength plus an integer multiple of wavelength, then we get destructive interference or cancellation. I.e.,
\[ \sin(x + \frac{2\pi}{2}) = \sin(x + \pi) = -\sin(x) \]
that's a wave which varies by half a wave length from sin x, and notice now that
\[ \sin(x + \frac{2\pi}{2}) + \sin x = 0 \]
i.e., destructive interference.

Answer 3

Hence, any variation of length of the alternative paths results in interference, be it twice or long, or 1.000001 as long, or 1/100000 as long, or 10^23 as long. What's important is the device is superimposing two waves on top of each other and that results in interference.

Answer 4

Make sense?

Answer 5

Thanks James. I have been reading some quantum physics (David Deutsch) and I am trying to rationalize his "many universes" approach to QM.

Answer 6

The Michelson interferometer is the most common configuration for optical interferometry and was invented by Albert Abraham Michelson. An interference pattern is produced by splitting a beam of light into two paths, bouncing the beams back and recombining them. The different paths may be of different lengths or be composed of different materials to create alternating interference fringes on a back detector. Michelson, along with Edward Morley, used this interferometer in the famous Michelson-Morley experiment (1887)[1] to show the constancy of the speed of light across multiple inertial frames, which removed the conceptual need for a luminiferous aether to provide a rest frame for light. i got this on net which might be useful to u. and i think u also got the answer for your question from this