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If a beam of light is travelling in full vacuum in same medium ,then , the energy of the light beam will decrease or not while moving through space ? The wavelength of the beam of light will change or not ?

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An electromagnetic wave will typically not decrease in energy if it travels through a vacuum. It will however diverge meaning that it will spread out over a larger area if travelling further. If it travels through a medium it may experience a loss in energy, or rather the medium will absorb it, since energy is never destroyed.

The wavelength of it may shift depending on the circumstances, redshift from distant celestial bodies is one example of such a shift in frequency.

Here below is a very rough sketch, consider the black square as being of the same size. Even though all of the energy in the wave is still very much in existence, the intensity on the square is lowered, $\frac{W}{m^2}$.

enter image description here

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