There is always a tragic element to law enforcement that we who are outside the world where people wear guns to work do not usually think much about.

This is especially hard when we have a shooting death like the one two days ago in Brooklyn, where a man was killed by police officers who say that they thought a fake gun he possessed was the real thing.

Some witnesses say different. They say that when the man, who had been in a trivial argument, turned around and raised his shirt to show that he had no gun, the cops opened up and brought his life to an end. Out of seven shots, he was hit three times.

From what we know at this point, there should be some controversy there always should be. Those who arrive at work armed or go about their tasks with the understanding that they might have to face death or make decisions that can lead to the death of a suspect on the spot have to be put under the microscope when blood is shed.

But there are things we should look into after the speeches are done and the rabble has been roused or calmed, after the placards have been put away and the sentimental images of cops as Boy and Girl Scouts with badges and 9mm pistols have drifted off.

We need to know what killing someone does to a cop.

I first truly thought about this some four years ago, when I was looking at “Memphis PD: War on the Streets,” an HBO documentary in which cops were talking about the psychological horror of having shot someone to death. I realized then that most of us have no idea just how heavy a police homicide is on a cop.

One of the most powerful images in that documentary was of a black cop obviously in awe and shock at what his job had demanded of him that day. Unlike the case in those stupid films in which cops slay with the ease that a butcher brings to slicing off steaks, this was not a simple thing.

As one cop said to me, “This is one of the reasons that we don’t get paid enough for what we do. None of us ever want to pull out our guns. It doesn’t come easy to us. … Whenever you go into a potentially dangerous situation, you pray to God that you don’t get hurt and that you don’t have to hurt anyone else.

“And when it comes to killing someone, I don’t know anyone who has ever fully gotten over it. They live with that dead person no matter how bad he was until they join him.”

That is part of the tragedy of that so-noble profession, and it is something that we should never forget once the smoke has cleared and the cops have been cleared.