Sentences of the kind Venkatesh wants to know whether…are indirect questions.  In indirect questions if and whether are generally interchangeable. But the two words have a slight  difference in meaning and this results in one being preferred to the other in certain contexts. Whether clearly suggests an alternative – whether or not.

If doesn’t have this clear suggestion.  So in: We discussed whether the Indian government should openly support Malay Indians …If would not be used. (The point made here applies to other verbs with a similar import:  debate, argue, consider, etc.). So when the clause openly presents an alternative (You must inform by the 30th whether you are joining the tour or not), if will not be used.

In initial position if strongly suggests a condition, not an alternative.  So when an indirect question is fronted, it opens with whether. Whether he will agree is a moot point. (Not: If he will agree is a moot point.)

After prepositions only whether is possible. There was an interesting discussion on  whether India should go ahead with the nuclear treaty. (Not: discussion on if India…) This is because a preposition has to be followed by a noun phrase and a clause beginning with whether has a nominal force. This also explains why a clause beginning with whether can be a subject: Whether he takes up the job or not is beside the point or a complement: The question is whether he will keep his word. Cf. The question is this.  In both the cases considered above (after a preposition and in the subject /complement position) only whether is possible, not if.

Apart from these restrictions, it is sometimes noted that if cannot appear before an infinitive.  Michael Swan contrasts these two sentences: They can’t decide whether to get married or not. / They can’t decide if to get married.  The point here has nothing to do with if not being able to appear before an infinitive. Cf. If to postpone the wedding suits you, well, go ahead.  If this sentence does not sound quite good, that is because sentences opening with a clausal structure are not perfect. The clause has to be extraposed, i.e., shifted to end position. If it suits you to postpone the wedding, go ahead. Swan’s sentence is bad because the context suggests an alternative. If in initial position can only suggest a condition.

Besides the considerations noted above, there is one more. Where if and whether are equally suitable, if is found in informal situations and whether in more formal situations.

The Cambridge Guide to English Usage (Pam Peters, 2004) notes one more point.  If can lead to a certain ambiguity as in You will let me know if you are coming.  This could mean: ‘let me know only if you are coming.’ (If you are not coming, you don’t have to call me.) With whether the ambiguity is not found.  You will let me know whether you are coming. Here you will have to let me know whether you are coming or not.

Perhaps this is as good a place as any to say a few words on if-then. This pair is usually (and naturally) found in Mathematics, more especially in Geometry. Here is a theorem from A School Geometry by Hall and Stevens. If one side of a triangle is produced, then the external angle is greater than either of the interior opposite angles. 

Space being what it is that is how things are. (We can imagine other spaces with different properties. The space Euclid was describing - it is the one we are all familiar with – is called Euclidean space.) There is an inevitability about the whole thing. Not so in: If you are coming, call me. No need to put then here, before call. But that is what we do. Even while speaking of ordinary affairs and events, many speakers of IE have then in an if clause.
If you look deeper into Euclid you will find that in many cases there is no then even though the theorem begins with if.  Here is one. If two straight lines cut one another, the vertically opposite angles are equal.

Why do H&S use then in some if-clauses but not in others? Is it arbitrary or principled? Perhaps some interested reader will come out with an answer!

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