Question

why white light do not disperse in a glass slab while it disperses in a glass prism

Answer 1

Well, in fact, dispersion does occur when light is passed through a glass slab - it is just harder to observe that way. Lets summarize how this happens:

Refraction of light when it passes from one medium to the other obeys Snell's law, which states:

n1 sin(1) = n2 sin (2)

Where n1 and n2 are the indices of refraction of the two media, and 1 and 2 is the angle the ray of light makes with the normal to the surface in the two media. The index of refraction for air is (almost) 1, while for glass it is about 1.5 (or so). So, when light enters a medium with higher index of refraction, it will be bent toward the normal, i.e. end up closer to being perpendicular to the surface.

So far so good. But how does that explain the dispersion of different colors of light? The answer lies in n, the index of refraction. The index of refraction is not a constant, but rather varies with the frequency (hence, wavelength) of the light involved. So, different colors are bent by different amounts. So, in a prism, light goes through two surfaces, which are not parallel and as a result, every color exiting the prism travels in a different direction - splitting up clearly over a short distance.

Now, for a slab the situation is different. Since the two surfaces are parallel, the direction of any color light is not changed by going through the slab - it is only offset by a small amount (that's exactly why objects look displaced a little when looked at through a glass slab). This offset depends on the angle of incidence, the index of refraction, and is directly proportional to the thickness of the slab. As a result, every color is offset by a very small amount with respect to each other, and the color separation is only observable at the edges, or if one uses a very small spot of light, and a very thick slab of glass.

Answer 2

In the case of a glass slab, the opposite sides are parallel and therefore different colors emerge parallel to each other and are seen simultaneously. Therefore, dispersion doesn’t occur in a glass slab. In a prism, the dispersion occurring at one face in enhanced by the refraction at the other face, but in a glass slab the dispersion occurring at one face is neutralized by refraction at the other face.

Hope it helps um