NASA Announces Asteroid Grand Challenge

One photon of light at wavelength lambda has energy hc/lambda and momentum h/lambda; in other words momentum = energy / c. If the asteroid is near earth then it's getting about 1kW/m^2 of light energy from the sun. So for each m^2 of area and each second of time, that's 1e3 / 3e8 kg m/s ~= 3e-7 kg m/s of momentum; if the asteroid is, say, 99942 Apophis then its mass is 4e10 kg; let's call it 3e10 kg, for a net acceleration of 1e-17 m/s^2 per square metre of area. If adding the mirrors replaces absorption with perfect reflection, then that's also the size of the change in acceleration they produce.

According to Wikipedia, which is always right (except when it's wrong), averting a collision t years in the future requires a velocity change on the order of 0.035/t m/s.

If we assume (this seems pretty damn dubious to me, but never mind) that the effect of our extra momentum from sunlight accumulates "perfectly" over time, and if we suppose we have 10 years' warning, and if we handwave away some details, then each m^2 of mirror gets us 1e-17 m/s^2 * 3e8 s = 3e-8 m/s of velocity change, and we need 3.5e-3 m/s. So we'd need about 10^5 m^2, or a patch 300m on each side. That's a lot of bees.

In practice, you won't get perfect momentum, and the asteroid may not always hold the same face to the sun, and the changes may not accumulate in the way you want and may be in an ill-chosen direction, and all the numbers above are only approximations, etc., etc., etc., so you probably need more than that to have much confidence of saving the earth.