This simulation shows the working of a lens made of a circular segment, that is, a disc cut by a straight line. The lens works here like the objective of a camera, by concentrating an incoming planar wave at the focal point of the lens. The index of refraction of the lens is equal to 5/3 = 1.666…, so that according the the lensmaker’s equation, the focal length should be equal to 1.5 times the radius of the circle.

Through the observation of tile patterns and the identification of the isometries involved in their composition, we intend to illustrate the natural connections between geometry and art and to provide a stimulating approach to isometries of the plane.