A 2D Demo for Spherical Mirrors in Excel – with virtual reflected rays

This is a demonstrative model for 2D spherical mirror ray tracing in Excel displaying both the real reflected rays and the virtual reflected rays. You you have the option of turning the visibility of the virtual rays off if you wish.  It works in Excel 2003 at about 40 frames per second and in Excel 2007 at about 4 frames per second. You can start it in  a hands-off demo mode by…

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Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 7

Based on the formulas derived up to this point in the series, this section creates an improved custom VBA function which calculates the x-y Cartesian coordinates of three points: the incident point, the terminal point of the real reflected ray and the terminal point of the virtual reflected ray. The structure of the  function is fairly simple and it is very easy to use too. The model is upgraded using the…

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Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 6

This section simplifies the formula for the Cartesian coordinates of the terminal point of the reflected ray and derives a very similar formula for a terminal point of the virtual reflected ray. In the next section all these new formulas together with some old formulas will be combined into a new user defined VBA function which will be used alone to trace the incident, the reflected and the virtual reflected…

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A Preliminary 2D Ray Tracing Demo for Spherical Mirrors in Excel

This is a demonstrative model for 2D spherical mirror ray tracing in Excel. It works in Excel 2003 at about 40 frames per second and in Excel 2007 at about 4 frames per second. You can start it in  a hands-off demo mode by clicking the “Fully Automatic Demo” button and at any time you can hit the the “Demo Style” button to choose a flexible (pulsating) mirror or a…

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Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 3

This section explains explains how to implement the formulas that define the emergent (reflected) rays into a custom VBA function. Though geometrically the last two presentation might look a little  elaborate, just be patient and follow the presentation, or even better try to just sneak peek and do it yourself. All this derivation is done based on first principles and some Mickey Mouse geometry. Take all the time you need, a day, a week…

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Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 2

This section explains the illumination setup by using an artificial star, derives the equations of the incident rays and also solves the system of equations for finding the exact coordinates of the points where the incident rays hit the mirror. Looking at the sign of the determinant of a quadratic equation involved in finding the intersection between an incoming ray and the mirror we can say if the ray hits…

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