“Was Rear Ended, And Received A 'following Too Closely' Tickt”

The other day I was approaching a traffic light [it was red, so I was stopping] when I was rear-ended by a lady. Her rear-ending me caused me to hit the person in front of me. There was no damage to the front of my car, nor was there damage to the bumper of the man's car I had rear-ended.

Now, at the time of the incident, the man who I rear-ended said everything was fine, and not to worry. However, today an officer showed up at my door saying he later went to the station and filed a report. He claimed that he was having back pains (which I think is fabricated, since the collision was so weak it was almost as if you wouldn't have known it occurred had you not heard a noise - and his kids were totally fine). At the same time, the officer issued me a ticket for following too closely.

Is there anything I can do to fight this, or any possible defence I could use? If you need me to write a more detailed account of the events I can, I'm just currently at work so I'm flying through this.

Thanks in advance for any advice.