I could go find the formulas and plug in the numbers , but I thought someone here might have already done so. I'm converting my headlights and fog lights to HID and my friends and I are arguing that I will lose lumens in the conversion. The original lights are 5000K 35W bulbs and I'm moving to 8000K 55W bulbs. Did this on a previous car and I find it brighter with a much longer throw distance.

How do I scientifically prove this?