When there is a lamp on a wall and the light from the lamp falls on the wall, we notice that the shape formed by the light is a hyperbola. I would like to know what the explanation for this is. Also, when you have a convex lens and you kee it flat on a horizontal surface, and sunlight falls at an angle on to the lens, you can see a curve of light on the surface that looks to me very much like a hyperbola. A hyperbola is the locus of a point moving such that the difference of its distances from two fixed points is constant. That makes sense when you're wondering why the locus of an interference pattern should be a hyperbola, because the path difference is constant. But I can't relate this to the phenomenon of light falling on a wall, or the lens thing. Thanks in advance!