Grand-dad may know them as fish-eyes, but these simple little convex mirrors can keep you from getting into deep trouble. Convex mirrors are an elegant solution to a complicated problem: How do you see around a corner without poking your head around to look?
Unless the entire upper half of your ride is made of mirrors and glass, then it has a blind spot where another car can hide without being visible to the driver through the mirrors. Blind spots come in two different forms: those caused by the viewing angle of the driver relative to the mirror, and those caused by the roof pillars of the car itself. This means you have two gaping blind spots -- one directly beside the car and another in the triangular area obscured by the car's rear-windshield post (referred to as the C-pillar).
Light bounces off a flat mirror the same way that a pool ball bounces off the pool table banks -- its angle of departure matches the angle of impact. So, if you're viewing a mirror at a 45 degree angle, then you can only see objects oriented at a 90-degree angle to your position (the angle of impact plus the angle of departure).
A convex mirror is a spherical section of mirror, meaning that it continually curves around the centre. As such, the angle of light reflection will change at any particular point on the mirror because the angle of that section varies relative to every other point. The end result is that the fish-eye mirror greatly broadens the viewing area, allowing you to see into the car's blind spots without turning your head.