# Resultant wave in the Michelson-Morley experiment

I was wondering when the two waves in the experiment, don't they lead to constructive interference? Consider the first case in the image. The two combining waves should lead to constructive interference.

Source: Wikipedia.

Edit

Sorry for the confusion. What I wanted to ask is what John replied. But John how will they have half the intensity. The wavelength will be the same and so the frequency even if the wave splits. But after recombination the frequency should increase. Shouldn't it?

• Well yes they do. If the original intensity is $I$ then each leg has half the intensity and they recombine to give intensity $I$ again. Apr 8, 2014 at 10:27
• You might note that the second image shows what Michelson and Morley expected to find, not what they did find. The horizontal path of the moving apparatus is contracted, so the two dots meet. Apr 8, 2014 at 12:55
• I am having a hard time understanding what is being asked here. The device is an interferometer, but they don't have any particular expectation about the initial state of interference (because they can't tune the length of the arms to the requisite precision). Instead they have an expectation about how the state of interference will change as they rotate the apparatus. So, what was the question? Apr 8, 2014 at 13:59
• I think the question is asking: "Shouldn't the purple dot go back towards the laser." The answer is yes, it probably should be going back towards the laser. But you shouldn't take simplified diagrams such as these too seriously. Apr 8, 2014 at 14:14
• @JohnRennie what exactly do you mean by intensity. I am only talking about the wavelength here. I hope I have clarified what I am asking. Sorry for the confusion. Apr 8, 2014 at 14:51