Finding the Point of Reflection on a Spherical Mirror
A geometric construction locating where a ray reflects from a sphere, making incidence and reflection equal
Under the note 'To the angles', Leonardo sets out a geometric construction for the point of incidence on a spherical body, given a visible object and the position of the eye. He draws the tangent line of equality m f, raises a perpendicular n g to the circle's centre, then transfers measured spaces and draws lines from the centre to obtain the ray of reflection b n and the ray of incidence h n, which he states will be equal. The sheet is filled with faint circles, tangents and triangles carrying these letter labels.
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Rays of incidence and reflection are equal at the sphere
Given the point of incidence on a spherical body, determined by the visible object and the eye, Leonardo constructs the ray of reflection b n and the ray of incidence h n and states that they will be equal. This embodies the equal-angle law of reflection applied to a curved surface.
Tangent, perpendicular and transferred spaces
He draws the line of equality m f tangent to the circle and, at the point of tangency, the perpendicular to the centre n g. He then takes the space n f and lays it in m n, draws from the centre to points m and n the lines g b and h g, and takes the space b f to lay it in m h.