How dense are Saturn's rings?

I assume that the A ring is the densest, but I might be wrong. Nevertheless, I failed to find any explicit information over the net about the minimum and maximum of densities for the different rings. As a less practical question: what would one see upon entering one of the denser rings? Would it be obvious that it is a dense but thin (few metres - 1 km) cloud of particles, continuously bombarding the spacecraft irregardless whether it orbits along within the ring, or one would not see more than just a distant haze (if lit by the Sun) that spans over the horizon?

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@RoryAlsop Would a 'what would this look like' include images, or something else? –  HDE 226868 Nov 4 '14 at 16:05
I was thinking images or a description, and to be honest, MBR's update looks like it could fit the bill, so unless a better answer comes along, he'll probably get the bonus. For some reason I wasn't expecting it to look like fog... –  Rory Alsop Nov 4 '14 at 16:19
@RoryAlsop Hadn't seen MBR's edit. Yep, that should be good. –  HDE 226868 Nov 4 '14 at 19:14
Thanks @Rory for raising the visibility of my Q! I'm not familiar with the bounty system, is it awarded when I accept an answer (and that answerer is awarded the bounty), or the bounty is independent of my decision? –  István Zachar Nov 6 '14 at 14:59
If you accept the answer, by default the bounty will go to that one, unless the bounty awarder decides to give it to another. –  Rory Alsop Nov 8 '14 at 15:02

It is not an easy question, as we lack of data to constrain strongly the density and mass of Saturn's rings.

However, a first clue of their density is their optical depth (that is a measure of the transparency of a medium). The densest rings are the one of the main ring system (rings A, Cassini Division, B and C) plus ring F; they are characterized by optical depth larger than 0.1 (up to about 5 for the densest part of ring B). Rings in the faint ring system (E and G) have very small optical depth (lower than $10^{-5}$).

With this regard, B is indeed the densest ring of Saturn's rings. (edit) Looking around ([1] and [2]) you can find numbers that help to figure out the density of this ring. Knowing its mass (about $2.8\times10^9$ kg) and its extend (from 1.527 to 1.951 Saturn radii, with a typical thickness of 100 m), you can deduce a mean density of about 0.0167 g.m$^{-3}$ (about $10^5$ times less dense than the terrestrial atmosphere at sea level).

Just for fun:

This gives you an idea of what means the optical depth. In the densest parts of ring B, optical depth is between 2.5 and 5, so you'll definitely notice you're in the ring. It is probably more complicated than that (with ring particles ranging from dust size to house size), but you get the idea.

Side note:

Optical depth is a measure of transparency of one medium; it measures how radiation is neither scattered nor absorbed by the medium. It expression is given by

$$\frac{I}{I_0} = {\rm e}^{-\tau}$$

where $I_0$ is the source intensity, $I$ the observed intensity, and $\tau$ the optical depth.

Sources:

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The denser rings are actually very comparable in mass density to that of air. Because of their larger particle/particulate sizes, the number density is much much smaller.

e.g.
Ring A: Radius ~ 137,000km, thickness ~ 10m, surface density ~ 20 g/cm^2
so a density of about 0.02 g/cm^3, which is about 10 times more than air, and 100 times less than water.