Foreign Key For Index Column - MYSQL If we have implemented Index on Primary key column in Table1 and on Referenced column in Table2. But we don't have Foreign key on Referenced Column. 

Can you please explain is this good to implement foreign key to utilize Index more efficiently
I might be wrong, but I don't think that the MySQL optimizer takes foreign keys into consideration. An index, on the other hand, may be very useful as a support for a foreign key. 

However, the main purpose of a foreign key is completely different than what you are asking for. The purpose is to keep the database consistent and maintain referential integrity. When deciding for or against foreign keys, I think this what you should be concidering.