Recent content by virgil elings

Maybe someone can explain the following twin paradox. There are two twins A and B. Twin A is shot straight up into the air with a very short and powerful cannon. Twin B remains on earth. Twin A goes up a distance and then falls back to earth. Which twin is now older?

nasu Sorry, I forgot to mention that f is the distance to the focal point measured from the on-axis surface of the convex side. This formula was derived for a beam parallel to the axis. I would guess that the focal point gets smeared a little for incoming beams not parallel to the axis...

The index varies as: n(y) = n(0) - f/t(sqrt(1+(y/f)^2)-1) where t is the thickness and f is the focal length

For a plano-convex lens try: r^2=(n^2-1)z^2 + 2f(n-1)z where r is radial and z is axial. At z<<r, this gives a spherical shape with f=R/(n-1) where R is the radius of the sphere. At r>>f, the shape is a straight line with r=sqrt(n^2-1)z You can derive all of this by remembering that the...