Question

If I poured water into my tea, would I see more or less of the bottom of the tea-cup?

Intuitively, there would be as many particles blocking as many photons, and so I'd see the bottom just as clearly as before

Answer 1

There is some misconception in Tims question already:

as many particles blocking as many photons, and so I'd see the bottom just as clearly as before

Blocking of photons will not impair clarity at all!

One has to distinguish absorption and scattering! Tea is a solution of some dyestuffs in water (optically) this dyestuff absorbs light of certain wavelengths (making the tea looking yellow/brown) but the tea is not made turbid ("Unclear") by that absorption. (Think of some color filter for cameras!)

The absorption is governed by Lambert/Beer law. The law shows, that doubling the length of the liquid column is "neutralized" by reducing concentration to half of original value.

Now the question of turbidity, In practice a tea may contain some particles from lime in the water, often some agglomerates from lime and some tanning agents in the tea. On top there is some fat/oil which drift as droplets or collect on the surface.

Any particle floating in the tea, which is about 50 nm up to some