Quick Michelson and Moorley question

[Precepts]

This may be hard to express without a diagram. For the beam that split left and came back towards the half silvered mirror perpendicular to the aether wind, shouldn't it be solved that way vectorially? My textbook has the speed of light (c) as the hypotenuse. Which has screwed me over in the way I think of it. Shouldn't the resultant velocity be the hypotenuse as the wind and the light beam meet at a right angle?

 

[sophiecentaur]

Hi
Without seeing your diagram, I can't be sure. The best way to deal with your problem is to look at other sources of the same information - for instance this link. There is a triangle which appears to be along the same lines as the one you are querying.
This is a very popular problem to discuss so you are bound to find what you want by Googling.
Alternatively, you can try posting a diagram of your specific problem. Do whichever is easier for you.

 

[John Huang]

This may be hard to express without a diagram. For the beam that split left and came back towards the half silvered mirror perpendicular to the aether wind, shouldn't it be solved that way vectorially? My textbook has the speed of light (c) as the hypotenuse. Which has screwed me over in the way I think of it. Shouldn't the resultant velocity be the hypotenuse as the wind and the light beam meet at a right angle?

I think before you can totally understand how a beam split itself, you should try to understand the definition of the speed of a beam (or a ray of light in the beam) if you can find one in any textbook.

If you cannot find one, try to define it by yourself. Your work will also help you to find out whether the speed of light in the second postulate of SR is referring to the speed of a photon in the ray or it is referring to the speed of the ray of light. One stone two birds.

I will like to discuss with you if your answer is different from mine.