program main
  implicit none
  real :: tol

  call my_sub()    ! Tol is not specified and some default value will be used

  tol=0.000005
  call my_sub(tol) ! Tol is explicitly specified

contains

  subroutine my_sub(tol)
    implicit none

    real, intent(in), optional :: tol
    real :: default_tol

    default_tol=0.000000001

    if (present(tol)) then
       default_tol=tol
       print*, "Tolerance IS specified by the user and equals", default_tol
    else 
       print*, "Tolerance NOT specified, using a default value of", default_tol
    end if

  end subroutine my_sub

end program main