Ignore time from date/time field, compare just date.
eg.
select convert(Datetime, CONVERT(VARCHAR(10),Invoice_Date ,105),105) as Invoice_Date
from tblInvoice
where convert(Datetime, CONVERT(VARCHAR(10),Invoice_Date ,105),105)>='8/01/2012'
and convert(Datetime, CONVERT(VARCHAR(10),Invoice_Date ,105),105)<='8/13/2012'
Happy Coding!
:)