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Let's say a submarine is coming to surface with a velocity $v$ normal to the surface of water and let's say you are the admiral of the navy viewing the submarine from the top. The submarine is exactly below you. Does the speed of the sub change or not?

I say it does not. It doesn't make much sense. While the speed of light varies, I don't think there will be a big difference in when the light reaches our eyes because the distance involved is very small compared to speed of light.

Bonus question: let's say you are no longer viewing the submarine directly below you as it comes normally upwards. Let's say that the sub is now moving obliquely to surface, or that you are viewing the submarine at an oblique angle or both. How will this change the velocity of the submarine when viewed above? I am sure it involves normal/lateral shift and probably long differentiations with respect to time. If its got long differentiate, I will put a bounty for it.

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    $\begingroup$ The speed doesn’t change, but whether you can estimate the speed correctly depends on whether you can account for refraction properly (or alternatively - what method you are using to measure the speed). You might want to make the question more explicit - for example, if you used laser Doppler to measure the speed with which the sun rises, does the refractive index of the water matter? $\endgroup$
    – Floris
    Commented May 17, 2022 at 19:58
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    $\begingroup$ It actually sort of does because depending on how you view it, the dimensions of the sub changes. Imagine painting the situation in different angles.. some the dimensions would be stretched. $\endgroup$
    – Cathartic Encephalopathy
    Commented Jun 27, 2022 at 20:31

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