I recently got in an argument with a friend while I was driving. When I moved to a different lane, I did not turn my head to check for any vehicles in my blind spot. Instead, how I checked was by leaning toward the rightmost region of the drivers wheel, looking into the left side mirror to see the field that is normally the blind spot. I've been doing this for several years, I imagine if I was wrong then surely I'd have gotten in an accident by now.
My friend, however, refuses to believe that works. He thinks the blind spot remains fixed no matter where the observer (driver) looks at the mirror or that at least it is not safe/effective as turning your head to look into your blind spot.
I understand mirrors in vehicles are convex mirrors, they slightly bulge out to increase the field of view for the observer (which is why objects appear closer in the mirror and why there is slight distortion). And I know as light hits the mirror, the mirror reflects it back outward. What I'm struggling with is how to explain that the position of the observer changes the blindspot.
How do I make my case mathematically?