Select from a huge table takes too long

[abdul Basit]

I have a table that has 1.2 million records. When I do a select using an alternate unique index it takes 15 to 30 seconds how ever using the primary index it takes less than a second. The two queries are as follows

Primary index is id which is an autoinc field.
cardnum is a long integer a secondary unique index

"Select id,cardnum from cards where cardnum=33333333333" slow

"Select id,cardnum from cards where id= 1270423" very fast

Running optimize does not fix the problem.

It it normal? What could be wrong.

Thanks