Physics Double Slit Experiment

The single slit is not needed if you are using a laser light for a specific frequency. Essentially, this is what the single slit does tho.

The role of the single slit is essentially to make the waves/photons reaching the a double slit be coherent with the photons/wave reaching the other double slit so that a good interference pattern occurs and can be observed.

The single slit makes the rays coherent in two ways. They make it coherent in a temporal manner (which is your constant phase difference) but they also make it coherent in a spatial manner which relates to the size. As the photons/waves reach the double slits they will be coherent which will make a good interference pattern for you to observe. If we used a precise laser of a specific colour and pointed it at the two double slit, then the single slit would be unnecessary because then the light coming to both slits is basically from the same source so similar spatial coherence and has a specific frequency + constant phase difference making it temporal coherent.
At this level, you do not need to be concerned about spatial coherence if you are studying A-levels.

At the time Young didn't have lasers so the easiest way to make a light source coherent was to use a single slit before the double slit. This is what he did and that's basically the purpose of the first slit.

Ah thank you! With regards to making the single slit wider, what does the paragraph mean by 'each part of it' I don't understand!

Ok, I will try to explain this simply. The book is absolutely correct but has worded it poorly.

If we make the first slit wider, the light can hit the second slit in numerous ways.But if the first slit is narrower, the light will have a few definitive ways in which they hit the second slit.
Essentially a light ray can pass through the first slit right through the centre or at the corners or at any point in the middle. So the light that goes to the second slit could have taken several different paths. All these different pathways light can take will mean that light from different pathways may interact/diffract/interfere slightly differently and in a more widespread manner. This makes you lose contrast between the lighter and darker parts of the fringe patterns. The light passing through the centre part of the gap/slit will diffract slightly to the right from the light that passes nearer to the edge.
Making the slit narrower basically, reduces the number of different pathways the light can take (because space is quantized) and the pathways are also closer. So the interference pattern is also less spread out and increases contrast.