1. The problem statement, all variables and given/known data The index of refraction of glass can be increased by diffusing in impurities. It is then possible to make a lens of constant thickness. Given a disk of radius a and thickness d, find the radial variation of the index of refraction, n(r), which will produce a lens with focal length F. You may assume a thin lens (d<<a). Note that there are two approaches to image focusing problems. You may be more familiar with one, where you would trace light rays using Snell’s law, and two rays converge to a point. This approach will lead to a very complex solution. 2. Relevant equations Snell's law: n1 * sin(θ1) = n2 * sin(θ2) 3. The attempt at a solution At first the problem seemed simple enough--just apply snell's law to figure out how to make the rays converge to a focal point F. However I realized a slab doesn't actually change the angle of the ray, (angle of deviation is 0). Though you can change the index of refraction at different points, the lens is thin so that in the region that a ray of light traverses, the lens will have essentially a constant index of refraction. I'm not quite sure how this lens would actually work. Also, what are the "two approaches" that the problem mentions? Thanks!