Light from a source A at (-1,1) is reflected by a plane mirror placed along the x-axis to a receiver B at (2,2) (a) For a given point (x,0) between A and B on the x-axis, find the distance between A and (x,0) and the distance between B and (x,0). Your answers should depend on x. (b) Denote by D(x) the sum of the two distances you found in the part (a), thought of as a function of x. Find D'(x). (c) Find the absolute minimum of D(x) on the x-interval [-1,2] (d) The light from source A reflected by the mirror to receiver B will travel the shortest distance possible (light will obey Fermat's principle). At what point P on the x-axis between A and B does the light hit the mirror?
Light from a source A at (-1,1) is reflected by a plane mirror placed along the x-axis to a receiver B at (2,2) (a) For a given point (x,0) between A and B on the x-axis, find the distance between A and (x,0) and the distance between B and (x,0). Your answers should depend on x. (b) Denote by D(x) the sum of the two distances you found in the part (a), thought of as a function of x. Find D'(x). (c) Find the absolute minimum of D(x) on the x-interval [-1,2] (d) The light from source A reflected by the mirror to receiver B will travel the shortest distance possible (light will obey Fermat's principle). At what point P on the x-axis between A and B does the light hit the mirror?
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Light from a source A at (-1,1) is reflected by a plane mirror placed along the x-axis to a receiver B at (2,2)
(a) For a given point (x,0) between A and B on the x-axis, find the distance between A and (x,0) and the distance between B and (x,0). Your answers should depend on x.
(b) Denote by D(x) the sum of the two distances you found in the part (a), thought of as a function of x. Find D'(x).
(c) Find the absolute minimum of D(x) on the x-interval [-1,2]
(d) The light from source A reflected by the mirror to receiver B will travel the shortest distance possible (light will obey Fermat's principle). At what point P on the x-axis between A and B does the light hit the mirror?
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