There’s a very interesting effect that occurs when you place a transparent object in a liquid having the safe refractive index. Ideally, it should vanish. In the real world, this hardly ever happens. There are several interesting effects:
1.) In general, although you can get the refractive index to match at one wavelength, it won’t match at all wavelengths (the substances are said to have different dispersions). Where the indices precisely match, you will get good transmission (not perfect – see below). Elsdewhere, you get scattering. The unexpected result is that you can see through in a direct line , but only in one color. Around the central region you get a sort of rainbow halo. This unexpected result is the Christiansen effect, named after (I kid you not) Christian Christiansen of Scandinavia. They used to use this effect for making bandpas filters, until they perfected optical coating techology.
2.) Even if you match the indices for several wavelengths, you still don’t get perfect transmission. Cal speaks from experience here. Although I could get solid lumps to “disappear” in a round container, if I put them in a flat-sided container with index-matching liquid, it would seem transparent only really close to an object. The farther away you got, the more translucent it appeared. If you were several inches away from a background object, it was like trying to see it through waxes paper.
Why?
Several reasons. For one thing, when you break up your solid material into many pieces, you almost invariably have some index variation from piece to piece. You get variations in bulk index, or the method of breaking it up causes stress birefringence. You get coatyings of dust or oil. Furthermore, small index differences don’t mean much at near-normal incidence, but as you approacj grazing incidence, even a tiny difference in refractive index will produce a noticeable optical effect. This is really the basis of the Christiansen effect – crumble up your solid phase into enough pieces and invariably you’ll have a lot of grazing incidence reflections causing scatter. In practical termsd, if you’re trying to be an invisible man in the fashion H.G. wells describes, by making yourself transparent with matching index, you’ll still be visible around the edges. Your skin will present a rainbow-like sheen around the edge. So will all your internal organs. You’ll look like a walking, iridescent Visible Man.
And that’s even when you can keep yourself from being covered with dust or water or paint.
Finally, a lot of substances have different refractive indices along different directions, and there’s nothing you can do that will match both directioons at once. You can see this effect with paper that’s got a drop of oil on it. The oil matches the refractive index of the cellulose fibers in the paper better than air, so you can see through the paper a bit, especially when it’s in contact with something. But you’ll never get it perfectly transparent. Even if you match the index in one direction in the cellulose fiber, it’s different in the other direction. (On top of which paper has sizing elements in it, bleaching agents, and often coloring agents as well. )