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"Whether" vs "If"

When “whether” is the word to be used only, and NOT “if”:

(1) After Preposition:

For Example:

We are concerned about whether John will be home safely from Iraq .

I will look into whether John would come.

The question of whether he should be fired needs more discussion.

(2) Before infinitives.
For Example:

John cannot decide whether to join the Army or to attend the college.

When “whether” is preferred over “if”:

(1) When a question-word clause is a subject or complement
For example:

Whether I have time to work on it remains a question. (Subject)

The question is whether I will have time to work on it. (Complement)

(2) When used with "or"
For example:

We have not decided whether we will go to the party or not. 

We have not decided whether we will go to the party or stay at home. 

(3) When the sentence is considered to be more formal.

For example:

Let me know whether you will accept the offer.
The head of our department will decide whether there is issue with investing in this product.

We will discuss whether he is suitable in this job.

Use if for a conditional idea, whether for an alternative or possibility.

For example:

Please let me know if you have any question.

=> It means: "I want to hear from you only when you have a question.".

Please let me know whether you have any question.

=> It means: "I still want to hear from you even when you do not have a question".  Please let me know either way.   

When “whether” and “if” can be used interchangeably.

(1) Whether and if both can introduce indirect questions, and a yes/no question.

For example:

I am concerned whether / if he can finish this in time. 

I don't know if / whether I will have time.
He asked me whether/if I recover from the illness.