Does recombination of light in a glass slab happens in the same way like in Newton's inverted prism experiment?

I know that refraction is due to different speeds of different wavelengths of light. So, How can those colors recombine to form a beam of white light (since different colors have different speeds)?

Is this image telling me the real fact?

The answer to your question is a little more subtle. In your picture, there is nothing but two prisms that are identical, and so the text is correct, this will not recombine the same white light that was originally separated into separate wavelengths.

Though, it is possible to recombine the white light in your case, but not with this setup. You cannot recombine the white light with just the identical prisms in your picture. You need a different way.

However, this recombination is impossible if only two identical prisms are used,9–11 as can easily be checked by applying Snell’s law to rays that enter and exit the faces of the two prisms, since the rays corresponding to each color emerge parallel to each other. It is possible to perceive the recombination of white light that has been initially decomposed by a prism by using more elaborate optical setups than the one (see Fig. 1) criticized in this note, including setups based on the use of a converging lens,4,14 mirrors,4,15 or more than two prisms.10,11

https://aapt.scitation.org/doi/full/10.1119/1.5018680

There are several ways to recombine, in one you need three laser pointers, and two prisms where the height is a little bit larger then the distance between the upper and lower stacked pointers.

In another setup that can recombine white light, you need a lens of focal length f at a distance of 2f from the first prisms.

The lens is required to bring the rays back together. It creates an image of the exit of prism one on the entrance of prism two. The figure below shows how Newton did it. White light enters at O, it is split and recombined by the second prism. The third prism splits the light again. This experiment demonstrated that white light is made from lots of separate wavelengths.

Is it possible to implement the reversed dispersion of a white light beam and how?

• On a broader technical setting, these are known as pulse stretchers and pulse compressors, and they are a critical ingredient in Chirped Pulse Amplification (also described here). In OP's case the white light is incoherent (no temporal coherence between the different wavelength components), while in CPA there is high temporal coherence (i.e. the light comes in pulses), and stretchers and compressors use the fact that the path lengths taken by the different colours between splitting and recombination are different. – Emilio Pisanty Feb 23 '20 at 13:45

No, As white light passes through the prism, it splits into 7 colours, then when again passed through the prism, it will recombine into white light