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It actually does. Kind of. (But it doesn't have anything to do with why it can be refracted.)

Light has no rest mass. But, light can never be at rest.

Light does however, have momentum. And when it is reflected/refracted, it will transfer some of that momentum to whatever it hit.

Also remember that forces act on pairs of things. Light can be deflected by gravity (which will change it's momentum); therefore it must produce a gravitational field (which will in return change the momentum of whatever deflected it). And of course gravity is proportional to mass.

Light which is moving towards and object will gain momentum, like a falling rock would. Only instead of moving faster (since it's at a fixed speed), it shifts towards higher frequencies. If you look at the equations slightly differently, you get gravitational time dilation.

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