A while ago I read a grammar book where I was said to use a definite article every time a noun is followed by a qualifying clause with OF or another preposition.
1.1 The first person to run the mile in under four minutes was Roger Bannister
It is said in the predicate who the person is so asking 'Which first person to run the mile in under four minutes?' would be incoherent.
1.2 The father of one of my students rang me last night
Again. We have a qualifying clause with OF. It wouldn't make any sense to ask 'Which father of one of your students' so we take THE.
1.3 That guy married the daughter of his bank manager
The same. Of course, It could be that the manager has two daughters or the other is already married or too young to marry or you don't know that there are two or it simply doesn't matter. The main thing is that the manager is the father of the woman the guy married. And it singled out by 'Of his bank manager', which is the reason why we take THE instead of A.
1.4 Cars are a major source of pollution in cities.
Why does it have an indefinite article? It's not just a source but the source of pollution. So it kind of shrinks the possible variants and we should take THE.
The same applies to the following case:
1.5 'I want to show you a photo of Jane and me.'
Why do we have an indefinite article here? It's a defined photo. Not just some random picture of strangers. A listener knows what the photo is about. But the sentence took an indefinite article instead and I wonder why. Of course, there could be lots of photos of Jane and Me in the album but as shown in 1.3 But it simply doesn't matter and our focus is that the noun 'photo' is defined by a qualifying clause.
I'm now trying to figure out some patterns and here's what I think:
2.1 I don’t like the sound of that school food…
Delete the last part of the sentence and it doesn’t make any sense. So we take THE.
2.2 Dudley gasped and fell off his chair with a crash that shook the whole kitchen.
It still makes sense even after omitting everything after 'crash' so we take an indefinite article.
Am I wrong and there is no such thing as patterns in this topic? Could anyone write down some thoughts about it? Thanks