What is the question? Is it:

(a) Where, if anywhere, do you have to be in order to see the mote; or

(b) If you see the mote, where does it appear to be?

Hi Chris,

Good questions.  We know we can see motes in light, especially sunlight and you are standing on a darker side.  I think, from the question the mote is suspended in the centre of the sphere

It feels as if (I'm trying to visualise it) the photons travelling from the mote to either eye will hit the surface of the sphere perpendicularly, so they won't refract, so it would appear to be in the centre?

But I'm quite prepared to be shown to be wrong 

As it happens I have a globe shaped storm glass* on my shelf, so I did a quick experiment swirling it around, it does appear that the crystals in the centre seem to be in the centre (just by the way they don't move when I spin it), and neither magnified nor minified(is there such a word?). Not very scientific though.  

* en.wikipedia.org/.../Storm_glass

I am inclined to agree, it is only an offset defect that would appear in the 'wrong place' but if there was any doubt, then you could immerse the whole thing in an oil of similar refractive index to the glass (a so called 'index matching' fluid or gel for the less runny ones ), and then there would be no beam bending at the surface.

Mike.

Andy Millar said:

It feels as if (I'm trying to visualise it) the photons travelling from the mote to either eye will hit the surface of the sphere perpendicularly, so they won't refract, so it would appear to be in the centre?

Yes, if you look radially. Away from that line of sight, the light could be refracted just the right amount to see the moat, but it no longer appears to be at the centre. Think of spearing a fish from above a stream.

But if it's at the centre of a sphere can't you only look radially at it? (Else you'd be looking past it!) That's what I was trying to get my head around, whether there's any way you can look at it that isn't perpendicular to the surface, and I can't think that there is. Hence it has to be a mote (nearly dimensionless) at the centre, that's the only case where that's true.

indeed - l am visualizing this to be like an extreme case of the convex lens where  the ray thought the centre of the lens, is the only one that still passes through the centre of the glass element regardless of angle of attack.
  The parts of the defect off centre will appear distorted by refraction, yes, but the true centre remains in the centre.

M.

Yes, I think that must be correct. Start with light being reflected by the mote. It must travel radially, so when it hits the surface of the sphere, it is perpendicular to it and must pass straight through without being refracted. So the conclusion is that however you look at the sphere, the mote is always there at the centre.

Caveat: the mote must be a true point otherwise light could travel from it other than along a radius.

Yes, I think that must be correct. Start with light being reflected by the mote. It must travel radially, so when it hits the surface of the sphere, it is perpendicular to it and must pass straight through without being refracted. So the conclusion is that however you look at the sphere, the mote is always there at the centre.

Caveat: the mote must be a true point otherwise light could travel from it other than along a radius.