Answer Happy

P is the left dot, Q is the right one.
In class, we will discuss spherical lenses and mirrors in geometric optics. A spherical lens is only an approximation to the ideal lens for focusing light from an object at P to an image at Q. This problem explores the shape of the ideal lens. A point source of light at P is located distance s = 10 cm outside of a large block of material with an index of refraction n=1.5. The image is to be focused at Q, a point distance s' = 20 cm inside the medium. n (a) Use Fermat's Principle of Least Time to determine the shape of the ideal surface for focusing the light. That is, find an equation that defines the shape of a surface for which all paths from P to take the same time. Your result should be a mathematical formula that gives the height y of the interface as a function of distance x along the axis. (b) The spherical lens that best approximates the perfect lens has a radius R given by 1 n-1 S' R What is the radius of curvature of the spherical surface that will best focus the light from P to point Q? (c) Plot the ideal surface and the spherical surface you found on the same axes. Discuss the similarities and differences between the two surfaces. n +