Convex mirror, and you point a light at it horizontally

[Alkatran]

If you have a convex mirror, and you point a light at it horizontally, does the light always reflect through the focal point? (the point halfway on the line connecting border and the center, parallel to the light's initial path)

I remember learning this, but I think of a mirror in the shape of a semi-circle, and you point the light at the bottom, it only bounces along the edge...?

 

[Doc Al]

Horizontal (parallel to the axis) rays will reflect from a convex mirror so that they appear to originate from the focal point.

 

[Gokul43201]

Also, this is only true in the limiting case when the size of the mirror (aperture) is small compared to the radius of curvature. So, when you take a semi-circular (actually hemispherical) mirror, it is no longer small compared to R. So, the behavior will be different, and hence glancing is not a violation. It's just outside the domain that the above rule applies to.