Derive the Law of Reflection, ui = ur, by using the cal
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Derive the Law of Reflection, ui = ur, by using the calculus to
minimize the transit time, as required by Fermat’s Principle.
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- Consider that the speed of light inside a block made of a certain material is proportional to theheight y measured from the base of the block. Show that light moves in circular arcs insideof this material. Consider that light travels the shortest path between two points (Fermat's principle).Consider a toric lens whose two surfaces are spherical and toroidal. The spherical side has a power of +4:0 D, while the toroidal side is described by +6:0 90= + 2:0 180. (a) Determine the power cross. (b) Find the Sturm interval for a point object at 20 cm from the lens.(b) How does the index of refraction relate to the speed of light in a medium? If the index of refraction of water is 1.33, calculate the speed of light in water. Give one application of total internal reflection.
- The two mirrors illustrated in the figure below meet at a right angle. The beam of light in the vertical plane indicated by the dashed lines strikes mirror 1 as shown. (Let d = 1.40 m and 0 = 36.0°.) Mirror 2 d m Mirror 1 (a) Determine the distance the reflected light beam travels before striking mirror 2. (b) In what direction does the light beam travel after being reflected from mirror 2? ° above the horizontalA ray of light crosses the boundary between some substance with n = 1.54 and air, going from the substance into air. If the angle of incidence is 29◦ what is the angle of refraction? Calculate to 1decimal.A scene point with coordinate (X, Y, Z) = (α, β, γ) in the world is perspectively projected into an image at coordinate (x, y) = (δ, ϵ), where both coordinates are given in millimeters in the camera coordinate frame and the camera’s principal point is at coordinates (0, 0, f). The camera reference frame is translated ζ mm in the negative direction along the z-axis relative to the world reference frame. What are values for the camera intrinsics and extrinsics? Show all your work.