I was thinking about the situation given my text about a plano convex lens which was produced with a manufacturing defect. It's plane surface is tilted outwards by a small angle 'z'. In the text its written that when a parallel light beam enters the lens parallel to x axis , it will still be able to focus it at: ##(R/(u-1) , -zR)## where u is refractive index of lens and R is the radius of curvature of curved surface of lens and lens is at origin with rays along x axis starting from negative infinity. How does this happen? My analysis: I think the tilted surface is just for bending the ray(refraction) by a small angle 'r' and now we have Plano convex lens with parallel beam of light at an angle 'r'.