Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
Optimization hinders evolution!
ME256 Variational methods and structural optimization Jan.-May, 2011
Instructor: G. K. Ananthasuresh, Room 106, ME Building, suresh at mecheng.iisc.ernet.in
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Homework #2
Assigned: Jan. 18th, 2011
Due: Jan. 25th, 2011
Points: 40
Additional points for work that is beyond instructor's expectation!
Look up Homework #1 of 2010 offering of this course and the solution posted there to know what is meant by "beyond instructor's expectation".

  1. 40 points
    This homework is concerned with geometric optics. In each of the following cases, pose and solve the problem. Verify with sufficient conditions to conclude if the point is a local minimum, maximum, or a saddle point.
    1. Reflection off a straight line from a point to another point in a plane.
    2. Relfection off a spherical concave mirror from a point to another point in space.
    3. Reflection off a right circular cylinder from a pont to another point in space.
    4. Refraction at the interface between two media from one point in one medium and another in the other, both points in a plane.