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what is the index of refraction of a medium in which the speed of this radiation is 2.54X10^8 m/s? I don't even know where to start...

Divide that number INTO the speed of light in vacuum (which is 3.00*10^8 m/s) and you will get the refractive index, N. That is how it is defined.

It will be greater than 1.

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