Convex lens and concave mirrors behave the same way. why? how

a convex lens flips an image as it passes through and produces a real image (i.e. it appears as though it is behind the lens). a concave mirror also flips the image and produces a real image.

A convex lens only behaves like a concave mirror (producing a real image) when the index of refraction of the lens is greater than the surrounding medium. If the medium and available materials to make lenses worked the other way around, then a concave lens would be like a concave mirror. Since the Snell's Law effect deflects light toward or away from the normal to the surface, depending on direction, it had to be one way or the other. Circumstances made it work out the way it is.

More interesting, I think, is that a thin spherical lens and a large radius "thin depth" spherical mirror each produce images at all.

A convex lens forms an image at da back side of mirror
whereas a concave mirror forms an image by reflecting da rays in front of the mirror