Answer Happy

Optics
Question 1 (a) [4 points] What is the optimum shape of a mirror used in an astronomical telescope? Use Fermat's principle to calculate the mathematical expression that describes this mirror (The optimum shape will focus light from a plane wave into a point source). Provide the equation for the mirror surface in two dimensions (e.g. x & y) (b) [4 points] Along the optical axis, the distance between the focal point and the mirror is a fixed length f. What is the separation between this focal point and the mirror along a direction perpendicular to the optical axis? (c) [4 points] A CCD camera is placed at the focal plane of the mirror. The pixel separation in the CCD is 10 um. What angular difference is measured from pixel to pixel due to the magnification of the mirror? (d) [4 points] If the focal length of the mirror (f) is 10 m, what is the smallest angle that can be resolved in the telescope (based on the pixel size of the CCD camera)? (e) [2 points] What is the curvature of this mirror at the optical axis? (f) [2 points] Even with an ideal mirror, the image at the focal point will not be a point. What physics will affect the size of the image at the focal point?