I'm doing my Bachelor's degree from photography. I noticed that my developed film Ilford HP5+ is not just black&white but it is slightly violet (as you can see on the left picture). Does it have anything to do with fixing time? I tried to find the literature why this happened, but didn't find any.
Its been a very long time, but I believe this is caused by inadequate rinsing of the negative during processing. The film has a coating to reduce light reflecting from the film backing itself. It is usually rinsed away, but seeing a slight purple tinge on negatives is likely very familiar to those who have developed their own B&W film. The coating is called 'anti-halation' coating.
As others have said, it does not impact the print image itself, since B&W paper can not reproduce 'purple'. If you are printing on a color inkjet printer from a scan, it may be reproducing the purple, since most CMYK inkjets simulate B&W using a mixture of CMYK inks (not just the K). A solution is to convert the image to B&W in your editing software, or use B&W/greyscale inkjet ink pots.
The color of a B&W negative is irrelevant unless you're using color print paper. If you have true B&W paper, then all that it cares about is the relative irradiance. You could print with any color negative and get a B&W image. If your print is what appears to be tinted, then either the paper is not what you think it is (e.g., there are styles which produce sepia-toned prints) or it's ancient and expired, or you've introduced a color overtone from some problem with the chemicals.
Each manufacturer uses a slightly different film base. Ilfords is slightly purple, Kodak's slightly cyan on some and Agfa had a slight green cast. This changes by film type as well within a brand. The color can impact the print if you use Variable Contrast paper. Fixing isn't usually a problem related to film base color. Kodak's Tech Pan was the most neutral as I remember. Most of the films I used are no longer available.
Early photo materials were not very sensitive to light. Additionally bright objects often imaged as a blurred splotch. This imperfection is called a halation. The solution is various colored dyes applied during manufacture. Dying light sensitive silver salt crystals changes their sensitivity and adjusts how they react to different colors. The problem of the halation is solved by an undercoat of dye. This dye is the color the film is least sensitive too. A UV blocking overcoat is also applied.
These sensitizing dyes and anti-halation dyes are generally water soluble. Therefore they will wash away during the processing steps. Some, however, are stubborn and these linger. They will eventually wash out given time. These give the processed film a tint that is uniform thus harmless. The main effect is cosmetic. If you are making chemical prints, the dyes block some blue exposing light -- thus they add a smidgen of extra print time.
If you are a purest who hates the coloration these dyes can induce, then add time to the fix and or the wash stage to give further time so they can wash away.
The breakthrough came in 1873. Hermann Vogel, Professor at Berlin Technical, wanted to solve the halation problem. He reasoned that light was being reflected within the emulsion. He has a student dye an emulsion yellow. This prevented the halation. To his surprise the emulsion gained green sensitivity. Over time, his graduate students experimented with sensitizing dye and gained sensitivity to red.
During exposure light travels through emulsion, bounces back from the backing layer and exposes the emulsion again, this time with blurred light, adding halos to the image.
This reflection can be prevented by adding opaque dark layer behind the emulsion. Due to the nature of b&w films, the layer is made of soluble dye.
Most of the dye is removed during processing, but usually not all and some residual coloring is normal. Amount of the coloring will vary depending on used processing chemicals and time of processing. You don't see this coloring with other types of films, because they use silver based or pigment-based anti halation layer that is not possible with b&w negatives.