The Inverse square law of light

In the introduction to the book, Kepler spoke of another discovery he had made: the inverse square law of light. If a burning candle is set on a table, the lighted area surrounding it on the table is circle, with the candle in the center of the circle. Kepler, thinking in three dimensions rather than two, reasoned that light starting from one point in space )the candle flame), spreads out not just in a circle but in all directions, in the form of a sphere. Wherever you are, within reach of the light, you can think of yourself as being at the edge of a sphere centered on the light source. Wherever you are, within reach of the light, you can think of yourself as being at the edge of the sphere centered on the light source. Someone a little farther away can also imagine himself or herself being at the edge of a sphere centered on the light source. At that second location, the sphere is bigger, and the light looks dimmer. How much dimmer? Was the question. Kepler reasoned that the light’s brightness was related to the size (the area) of the sphere. If two observers were both looking at the light, the observer B was twice as far away as observer A, then observer B’s sphere was four times as large as observer A’s sphere. B saw the light only a fourth as bright as A did. If B was three times as faraway as A, B’s sphere was nine times as large as A’s sphere, and B saw light only a ninth as bright as A did. As Kepler’s inverse square law of light states, the intensity of light is inversely proportional to the square of the distance. The square of two (two times as far away from the light source) is nine and so forth.

In January 1604, a little more than a year after the Christmas for which he had promised it, Kepler presented the completed manuscript of “Astronomiae Pars Optica” to the emperor, and the book went into publication. The ideas and discoveries about light and optics that Kepler wrote about in this book and later applied to the telescope in another work, ‘Dioptrice,’ became the foundation for seventeenth-century optical theory. ~ Page 293