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A hollow prism itself cannot disperse light when kept in air.

But can it disperse light when immersed in a liquid that has different refractive index than air and the material of the prism?

By hollow prism I mean something like this enter image description here

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    $\begingroup$ I don't actually know the right answer, but I think that you will get dispersion just as in the case of a "normal" prism because of the change in the refractive index (and taking into account the effect of the walls of the prism and their width). $\endgroup$
    – JackI
    Dec 23, 2016 at 5:29

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Short answer is yes. Hollow prism will disperse light if immersed in water. JackI's comment is absolutely correct.

Dispersion happens when the light trespasses the boundary between water and air because refractive index of substances depend slightly of the light color (wavelength). In case of hollow prism immersed in water light still trespasses boundaries between water and air, so there will be dispersion.

UPDATE.

Short answer: this prism will disperse light when immersed in water.

More details.

Let's see what happens when light goes through a piece of glass with parallel surfaces. Originally a beam of light consists of electromagnetic waves of different length, but the direction of them is the same.

Beam trespasses air-glass border. And now the beam gets splitted into several beams consisting of light of different color. This is because refractive index of glass depends of the light color.

Next each of the colored beams goes out from glass. (note, that beams of different colors would reach the other surface of glass in different points!) If there is the same substance "after" the glass as there was "before" the glass, the direction of each colored beam would become the same as it was before the beam entered the glass. All the colored beams would be parallel, but actually there will be some distance between them now. Thicker the glass - bigger the distance between beams of different colors. If you take thick piece of glass you would be able to see this effect with naked eye.

But if the glass is not thick enough you would not see it.

Situation is different if the substance "after" the glass is not the same as "before". Each colored beam would change it's direction when coming out from the glass, but the new direction would not be the same as direction of original beam. And the colored beams would not become parallel.

The direction of the beam after trespassing layer of glass does not depend on glass properties (unless light reflects from it), it only depends on refractive index of the substances "before" and "after". If the glass is not very thick situation is as there were no glass at all. (All said is true only if glass forms a layer: it's surfaces are parallel).

So in the air the hollow prism would split white light beam into several parallel colored beams. Effect would be small if prism walls are thin.

In the water situation would be different. White beam enters glass, get's splitted into colored beams, each beam goes from glass to air, change it's direction once again, but the colored beams would not be parallel. They diverge more and more, each beam enters second glass wall, changes direction, leaves glass and enters water changing direction one more time. Beams of different colors would not be parallel after that. The picture would be very similar to a picture of light going through the regular prism in the air.

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  • $\begingroup$ What do you mean by boundary between water and air? Do you mean glass-air? The only boundaries are water-glass, glass-air, air-glass, and glass-water. Should I add a diagram? $\endgroup$ Dec 23, 2016 at 9:54
  • $\begingroup$ I have misunderstood you question a little bit. I imagined just water with a cavity inside in a form of prism :) But all my point remain the same if the immersed prism has glass walls. $\endgroup$
    – lesnik
    Dec 23, 2016 at 10:21
  • $\begingroup$ I have added a diagram. Note that now, there will be no dispersion if kept in air, as rectangular glass slabs do not produce dispersion. $\endgroup$ Dec 23, 2016 at 13:53

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