What is the principle of acid-fast stain?

Acid-fast stain is a type of differential staining technique that is used to study acid-fast bacteria that belong to the genus Mycobacterium.  These bacteria have a high concentration of waxy mycolic acids in their cell walls, which prevent any stains from penetrating and discoloring the cell. When carbol fuchsin stain is applied to the smear, it solubilizes the lipoidal material present in the Mycobacterial cell wall. When heat is applied, the stain penetrates further through the wall and enters the cytoplasm, staining the whole cell a red color. On application of a decolorizing agent, acid fast cells remain red in color. This is because the decolorizing solution cannot penetrate through the large amount of lipoidal material in the cell wall of acid fast cells. On the other hand, non-acid fast cells are easily decolorized and become colorless on application of a decolorizing agent. This is because the lipoidal material is absent in their cell wall. When a counterstain such as methylene blue is applied to the stain, only the decolorized cells that absorb the counter stain appear blue while acid-fast cells retain the red color.