Why is a spectrum formed by a prism and not by a glass slab?

Answer 1

Light travels at different speeds, depending upon the medium. Light traveling through a vacuum goes at a rate of about 300 million meters per second, but it travels more slowly through matter because the energy is absorbed by molecules. In some cases, that's all there is to say. However, in transparent media like air, water, and glass, the energy of the light is absorbed and then re-radiated to the next molecule, and the next, and so on, until it emerges from the other side. The degree to which light slows down in a transparent medium is related to what's called the "refractive index" of that medium.

White light is made up of what we perceive as different colors, and each color is characterized by an electromagnetic wavelength and frequency. It turns out that these colors travel at different speeds (are refracted differently) in transparent media. But it's a small difference. So if you shine a white light through a window pane, your friend on the other side will see a white light.
The triangular shape of a prism matters if your aim is to create a spectrum. As I said, the different colors travel at different speeds through a medium like glass. A prism standing on its base is narrower at the top than it is at the bottom. This means that a beam of light travels through different thicknesses of glass. Since some colors move a bit slower than others through glass, the difference in distance causes a delay, and we see a spectrum. Basically, the prism amplifies the differences in speeds of the colors. Violet (at higher frequency, shorter wavelength) is slowest.

Answer 2

White light is a combination of all of the seven colors that we see in the visible-light spectrum. In a prism, the white light enters at an angle and is then dispersed into a spectrum. This happens because each of the different frequencies of light that compose white light have slightly different values for their indexes of refraction. The index of refraction is just the proportionality constant between the speed of light in a vacuum and the speed of light in a material, but it's value is different for different frequencies and different materials. The result of these frequencies all having different indexes of refraction is that they all slow down to different speeds. This is seen as a bend in the direction of the incident ray, where the different frequencies all bend at different angles.

Now, if the edges of the prism that the white light is traveling through were parallel, the dispersed light would bend back into white light as it left the prism, and then continue on traveling at the speed it was going before entering the prism. This is why the sides of a prism aren't parallel. The non-parallel sides of a prism don't prevent the light from bending back, but they do force this bend to occur at slightly different times, thus maintaining the effect of a spectrum as the light exits.

This same concept happens to light as it travels through raindrops, which is what produces rainbows.