Reflection: where light rebounds at equal angles
A compass construction of the equal-angle reflection point, with an expense note and a column of figures
The left page carries a lettered circle-and-arc diagram beneath a long passage on reflection, and the right half is filled with a dense fan of ruled rays sweeping through a focus among concentric arcs. Leonardo constructs, with the compass, the point where light from a striking at o rebounds between equal angles to c, and observes that the brightest point shifts with the positions of the eye or the light while the shadow stays immobile. Among the studies are a one-line note of money spent — on a quilt and on redeeming the rings — and a short column of arithmetical figures.
On this page
Constructing the angle of equal-angle reflection
From the line a b a semicircle is drawn whose centre is then moved from intersection b to o, and a further arc n b m is struck through both intersections. Where it cuts the proposed circle at o lies the sought angle, where light from a striking at o rebounds between equal angles to the point c.
The brightest point moves; the shadow stays fixed
Leonardo adds that the position of the brightest point falls in as many places as there are positions of the eye or of the light, while the shadow is always immobile. Whatever change the eye makes, it still sees the shadow.
Semidiameter and intersecting circumferences
A marginal note repeats the opening of the construction: with the line a b make the semidiameter of a circle. It restates the compass work of intersecting circumferences used to locate the reflection point.
Fan of rays converging to a focus
The right half is filled with a dense fan of ruled straight lines sweeping through a focus among concentric arcs. It illustrates rays converging, of a kind with the reflection study opposite.
Note of money spent
On the right-hand page a single line records money spent — on a feather-quilt and on redeeming the rings. It is a personal expense memorandum set among the geometrical studies.
Column of figures
A short column of numbers and operations stands at the lower left, setting out values such as 70, 49, 31, 18, 13 and 21 for calculation.