did something ridiculous, think i've burnt my alternator out

Just bought a new battery for my 1980 series 3 petrol, and like a total moron, I hooked up the terminals the wrong way around, causing smoke to start coming out of the back of the alternator. Now the alternator is not charging anything, and the battery light comes on only when the ignition is off. I'm thinking it's fried, and I'm not too good with electrics, which is completely evident from that fact that I've had to post this

I do have in my posession, a lucas a127 65amp alternator, and I was wondering if that would fit in to this vehicle. It's actually Syphers alternator, spare from his old 19J engine, so if it would fit, I'll have to see if he'll let me have it off 'im

any tips appreciated!

Check the pulley is about the same size, but if it fits it should work just fine.

Thanks for there reply Well it definitely fits, and looking at the voltage when I rev it up it sends to be working (15v almost). the thing is, my battery charges light stays on on the dash until you're doing quite high revs, say about 40mph in 4th gear. Looking at it with my multi meter, it looks to be charging OK. The battery is brand new fully trickle charged and that gives out 13 volts on its own, then it's more like 14.5 when the engine is running. what causes the light to stay on? weird