Every time my subwoofer hits my cars lights will dim.

Sorry. Let me fix this. I have 2 spx audio 12" subs hooked up to 1 1200 watt American legacy amp. I recently upgraded all of my wiring to 4 gauge ( the power wire to the amp, the ground wire from the amp to the chasis, the ground wire from the cars bAttery to the engine, engine to chasis) wire throughout the whole car. There is a 40 amp fuse up by the battery and a 30 amp fuse in the amp. Every time that I crank up my
Music and I get a big hit, all of my cars lights will dim. I also have the highest alternator you can get for my car.

You need a cap, maybe 2.

I already have one. It's a 1.5 farad.

See: Powerful alternators for auto sound (http://www.zena.net/htdocs/alternators/AutoSound.shtml)

I already have one. It's a 1.5 farad.

That still may not be right.
Where is it installed? What formula are you using to determine what size cap you need?

It is installed before my amp coming directly off the line that goes from my battery about 2 feet away from my amp. I did have an 80 amp fuse up by my battery but then I changed it to a forty and it did a whole lot better. It used to have a 20 amp in it and I am considering putting a thirty amp in it. The fuse that keeps blowing is the one on my amp.

OK...
What size alternator is installed?

1200 what? Yep, I know it's 1200 Watts, but there are so many way of being deceptive. If it doesn't say something like 2 x 600 W RMS into 4 ohm, both channels driven from 100 Hz to 20 Khz or something on those lines, it's being deceptive.

What is the fuse on the AMP?

1200/12 is 100 Amps and there is an efficiency number of the power supply too. One might assume 90%. That ups the current that needs to be supplied.

Changing the fuse to a lower rating essentially puts in a high resistance. It's like having a short length of thinner wire.

The voltage across a cap can't change instantaneously. That's the definition of a cap. If the amp drains the cap, then the system has to supply a much greater current to recharge the cap. This taxes the electrical system even more.

I'll leave you with: Car Audio Power Capacitors (http://www.caraudiohelp.com/newsletter/car_audio_capacitor_myth.htm)

For now, I think the alternator is undersized.

I will look in the morning and see. I am just a little curious as to where it would say how big my alternator is. I do know that when I went to my Toyota dealer to get a bigger alternator. They said that it was the biggest that they had already in it. It does have a metal plate on it though that says 12v counter. I am assuming that that means it's 12 volts and it spins counter clockwise but again I will look in the morning.

That's true what Toyota told you. What you driving?

A 1999 Toyota celica hatchback.

I did look at the metal plate and it was too worn off to make anything out. Can I take it somewhere to see if it can be upgraded. Like can someone teat it to see exactly what it's specifications are?