How much air would be needed to block sunlight?

Was watching a sunset on the sea, I was wondering what would be a lower bound for the thickness of air needed to almost completely obscure the reddish light of the sun, or at least to make it impossible to distinguish the sun's shape. I was not able to wrap my head around google results when it comes to optical properties of air, so I'm at a loss.

Let's assume red light with a wavelength of around 650 nanometers, dry air at 1 bar of pressure, temperature of 20° celsius.

• What google results? – sammy gerbil Jan 7 '17 at 3:51

The number of interest is $5.893\times 10^{-3} ~\rm{/km}$ - the "Rayleigh attenuation coefficient at sea level for 0.65 micron light."
Now the eye is pretty good at making out the shape of a circle in the presence of background haze - let's assume that your criterion is met when you have reach 99% attenuation (1% of sunlight still going, 99% scattered into $4\pi$. Then the thickness of the layer of clean dry air at atmospheric pressure that you would need is computed from
$$0.01 = e^{-\mu t}\\ -\mu t = \log{0.01}\\ t = \frac{\log{100}}{\mu}$$
When $\mu = 5.893\times 10^{-3}$ km, the thickness of air needed is about 800 km