Approximation question -- How does this approximation simplify the integral?

[RF_FAN]

how does this aproximation reduse the integral

 

[mfb]

Where are lambda and k_z in the integral?

The approximation simply assumes the integrand to be constant, evaluates it at the midpoint (z'=0) and multiplies it with the range z' takes.

 

[RF_FAN]

so its because r'=0 ??
then why we need
l<<lambda kz<<pi
?

 

[mfb]

The exponential function should not change its argument too much, so kzl/r should be small compared to 1.