It's not just a matter of impurities, it's the physical properties of the material making up the sand. The most obvious one is the refractive index. At first it doesn't seem like that big a deal because water (1.33) doesn't seem that different from clear silica (1.52), and silica is used for optical glass, but the important thing to remember is that the refractive index kicks in when light transitions from one material to another. When you look through a body of water, you're only looking at one location where the light is "bent", namely the interface between the body of water and the surface. But if you weren't looking through a single interface, then things become a lot more complicated.
For instance, look at this image:

You can't see through relatively thin layers of water making up the waterfalls and rapids because you aren't looking at one transition where light gets refracted, but many as water and air are mixed and any given light ray transitions between water and air and back again many times, effectively scattering it. The total combined refraction means the material becomes opaque.
Here's another example from underwater:

Notice how the mass of bubbles completely hide what's behind them. It's not a matter of the bubbles individually being hard to see through; after all, they're composed simply of air which, in the total amount present, would be totally transparent. It's all the refraction between individual bubbles and the water which causes the scattering of light which makes the whole thing opaque.
The same thing would happen if you had a bowl of optical-grade glass grains. Even if each grain was optically transparent by itself, the total refraction of all the transitions between glass and air would combine to make the material in the bowl opaque.
In fact, here's a picture of that very thing:

And the smaller you make the glass particles, thus creating more and more surfaces light is refracting through, the more and more opaque the material becomes:

Eventually, finely ground glass looks like a plain white powder like salt, sugar, or talc.
The only way your desert could appear transparent is if the material making it up has a refractive index exactly identical to the air, fluid, and any other material that may be between the grains, which all have to be the exactly the same as each other as well.
ADDENDUM
Even given the above, just because you have materials with the same optical properties doesn't guarantee transparency because you need near atomic-level matching perfection at the interfaces. Any kind of imperfection will result in diffraction and scattering. For an example, consider automobile safety glass.

The exact same material as perfectly clear glass, only now it has fractures in it, and those fractures cause interfaces within the material itself where diffraction happens even though the material on both sides of the fracture is exactly the same. The result? Harder to see through. Enough fractures in three dimensions and on a small enough scale and you can't see through it at all, even though the fragments are right against each other. Internal fracturing is why, for instance, otherwise perfectly pure silica, calcite, or salt crystals can look cloudy.
Long story short, not only would all those materials making up the desert have to have the exact same optical properties, each would have to have homogeneous internal structure as well. So yeah, good luck with that.