Which is correct of the following:
If you're interested in the field of chemistry or biology, this programme is for you!
If you're interested in the fields of chemistry or biology, this programme is for you!
Logically, it seems alternative 1 would be the correct one, since it's either or (and therefore just one field per option), but the more I think about it, the more uncertain I become. Please help!
Both can be correct. Many meanings are possible, and more clarification might be needed.
If you ask "Would you like apples or oranges," then you could be offering someone an exclusive choice—if they choose apples, they get no oranges—or an inclusive choice ("We have fruit, would you like some? Some apples, or maybe some oranges?"). In logical terms, there is the OR gate, which can be satisfied if one or both of the options are met, and the XOR gate, which is satisfied if only one of the options is met.
But this is splitting hairs; most reasonable people, hearing the sentence "If you're interested in the field of chemistry or biology..." would interpret the or as and/or, especially since the context communicates that the programme is of interest to both—that is, they would assume an inclusive or. I doubt any editor would flag either field or fields as wrong in this usage. If it is very important to you to enforce a restrictive meaning, it's best to include additional clarification: "If you're interested in the field of either chemistry or biology."
One could also argue that "chemistry" and "biology" contain many "fields," like organic chemistry or marine biology. In this case, "the fields of chemistry or biology" could mean "the many fields of which chemistry and biology are composed." If this is intended, of course the plural is appropriate. But at the same time, few reasonable hearers would assume this meaning. If it is intended, additional clarification like "the many fields of [or within] chemistry or biology."
You were right first time. It should be (1). What you have done is to effectively leave out some words.
If you're interested in the field of chemistry or the field of biology, this programme is for you!
If the programme is for someone interested in both fields then you would say
If you're interested in the fields of [both] chemistry and biology, this programme is for you!
