Translations:Fermat’s principle and reflection and refraction/26/en

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First let us give a graphic derivation of the law of reflection using Fermat’s principle. In Figure 20, ST is the trace (in the plane of the paper) of a reflecting interface that is a plane perpendicular to the plane of the paper. Points A and B are any two points in the plane of the paper above the plane ST. Point Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle A^'} is the image of point A with respect to the plane ST. It is located by drawing Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle AA^'} normal to ST and making AD equal to Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle DA^'} . Draw the straight line Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle A^'CB} , which cuts the line ST at point C. Let Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle C^'} be any point whatever in the plane ST that is not coincident with C. (Note that Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle C^'} is not necessarily on the line ST.) Then ACB and ACFailed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle C^'} B are two conceivable travel paths from A to the plane ST to B.