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In the Michelson Morley experiment, the light from a source is passed through a semi-silvered mirror from where a part of it moves horizontally towards a mirror(from where we calculate t1) and a part vertically towards another mirror(from where t2 is calculated). Now t1 is calculated in the same frame where the experiment is performed but t2 is calculated from the other. I want to why we have to calculate only t2 from the other frame?

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Since you haven't made clear as to what $t_1$ and $t_2$ are, I'm assuming that they are the times takes by light to cover the paths of the interferometer. Now, coming to this question, there is absolutely no bar as to what frame one should choose to calculate either of the times. Consider two paths: 1 and 2. Say ether wind is along path 1, then in Earth's frame: $$ t_1 = \frac{D}{c+v} + \frac{D}{c-v}$$ and in Ether frame: $$t_1^g = \frac{D+vt_1^g}{c}$$ which is the time for light to go from glass(semi-silvered) to mirror and $$t_1^m = \frac{D-vt_1^m}{c}$$ which is the time for light to go from mirror to glass. So, $$t_1 = t_1^g + t_1^m$$

Whereas $t_2$ calculation is the same in both frames if path 1 is where the ether wind is.

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