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British Library, London — Arundel MS 263

0087 v

Figura con lettere.

Qui si dimostra come il concorso de' razi refressi non passa il 4° del diamitro delle spere donde li spechi concavi hanno la loro curvità, come si dimostra nella linia a o.

Figura con lettere.

Se si volessi vedere e' razi seperati, sia tolto lo spechio in figura d'un mezo anello il quale sia piano di dentro, di poi s'è fatto una mistura di biacca tenperato con uovo, e con quella coperta col penello due o tre volte, e secca ch'elle sia, sgraffiata e scoperto lo spechio collo stile di legno aciò non graffi lo spechio, e così vedrai li razi seperati sopra il piano a b c, come son seperate le lor cause.

0086 r

Figura con lettere e numeri.

Sotto la figura:

Se questo spechio sarà fatto in figura d'un mezo anello, piano e lustro di dentro, e che sia tutto ocupato di dentro dalla pariete c d, salvo un minimo spiraculo in d, allora fie veduto il sole spechiato in tutte le sua risaltazione, come in c, e, f, g, h, i, K, L, n; e tutto il resto dello spechio sarà oscuro.

A lato della figura:

Infra li spechi concavi di pari diamitro, quello farà il concorso de' sua razi refressi più disuniti e di minore caldeza, il quale fia di magiore concavità.

Questa magiore concavità predecta si pò astendere insino alla metà della spera donde tal concavità è causata, come si dimostra in c h d. Della quale per te medesimo puoi conosciere come la parte n c e d o sono di poca valitudine, perché il razo b o che lo percote nel punto o, balza in otto lochi, cioè di o in e, e di e in f, e in g, e in h, e in i, e in K, e in l, e in n; e mai s'interseca nella centrale del cateto m h.

Il secondo razo 7 e ancora lui è di poca valitudine, conciosiaché esso vada risaltando per la superfizie di tale spechio in men somma di siti; nondimeno ancora ch'esso s'interseghi nella centrale del cateto, essa linia è sola, e però poco vale.

Ancora il razo 6 f è poco valido, perché dopo la percussione fatta in f, esso intersega la centrale del cateto in un sol sito, e percote in K, e risalta inverso il sole.

Medesimamente 5 g, dopo la percussione da lui fatta in g, risalta in r.

Adunque di tanta concavità solo la parte i g è manco trista che nessuna dell'antidette da g in d.

Figure with letters.

Here it is shown how the convergence of the reflected rays does not pass the fourth part of the diameter of the spheres from which the concave mirrors take their curvature, as is shown in the line a o.

Figure with letters.

If you wish to see the rays separated, take the mirror in the shape of a half-ring which is flat within; then make a mixture of white lead tempered with egg, and cover it with the brush two or three times; and when it is dry, scratch and uncover the mirror with a wooden stylus, so that it does not scratch the mirror, and thus you will see the rays separated upon the plane a b c, as their causes are separated.

Figure with letters and numbers.

Below the figure:

If this mirror is made in the shape of a half-ring, flat and polished within, and is entirely occupied inside by the wall c d, save for a minimal aperture at d, then the sun will be seen mirrored in all its rebounds, as at c, e, f, g, h, i, K, L, n; and all the rest of the mirror will be dark.

Beside the figure:

Among concave mirrors of equal diameter, the one of greater concavity makes the convergence of its reflected rays more disunited and of lesser heat. This greater concavity can extend as far as half the sphere from which it is caused, as shown in c h d. From this you can know for yourself how the part n c e d o is of little value, because the ray b o that strikes it at the point o bounces in eight places, that is from o to e, and from e to f, and to g, and to h, and to i, and to K, and to l, and to n; and it never intersects the central line of the cathetus m h. The second ray 7 e is likewise of little value, since it goes rebounding over the surface of that mirror in fewer places; nevertheless, though it intersects the central line of the cathetus, that line is alone and so is worth little. Again the ray 6 f is of little worth, because after striking at f it intersects the central line of the cathetus in a single place, strikes at K, and rebounds toward the sun. In the same way 5 g, after striking at g, rebounds at r. So of all that concavity only the part i g is less bad than any of the aforesaid from g to d.

Separating the rays of a concave mirror

Where reflected rays converge, and an experiment to display them one by one on a coated half-ring mirror

Optics & Light

The left leaf (87v) states that the convergence of reflected rays never passes the fourth part of the diameter of the sphere from which the mirror's curvature is taken, shown along line a o, and describes an experiment: coat a flat half-ring mirror with white lead tempered with egg, then scratch the coating away with a wooden stylus so the rays appear separated on the plane a b c. The right leaf (86r) continues the experiment: with the mirror's interior blocked by wall c d except for a tiny aperture at d, the sun is seen reflected at each rebound c, e, f, g, h, i, K, L, n. A long note argues that among equal-diameter concave mirrors the more hollow one scatters its rays into eight weak rebounds that never cross the central cathetus m h, so only the portion i g is less useless than the rest.

To see the rays separated, take a mirror shaped as a half-ring, flat within, and cover it two or three times with white lead tempered with egg. When dry, scratch it clear with a wooden stylus, so as not to scratch the mirror itself, and the rays will appear separated on the plane a b c, as their causes are separated.

A tiny aperture at d reveals the sun's successive rebounds

If this half-ring mirror is flat and polished within and wholly blocked inside by the wall c d, save for a minimal aperture at d, the sun is seen mirrored in all its rebounds, as at c, e, f, g, h, i, K, L, n. All the rest of the mirror will be dark.

Greater concavity scatters rays into eight weak rebounds

Among concave mirrors of equal diameter, the more hollow one makes the convergence of its reflected rays more disunited and of lesser heat. Ray b o striking at point o bounces in eight places (o to e, f, g, h, i, K, l, n) and never intersects the central cathetus m h, so of that concavity only the portion i g is less bad than the rest.

Reader's Edition — described with AI from the e-Leo transcription.

0087 v

Figura con lettere.

Figura con lettere.

0086 r

Figura con lettere e numeri.

Sotto la figura:

A lato della figura:

Figure with letters.

Figure with letters.

Figure with letters and numbers.

Below the figure:

Beside the figure:

Separating the rays of a concave mirror

On this page

Reflected rays converge within a quarter of the sphere's diameter

Experiment: coat a half-ring mirror to see the rays separated

A tiny aperture at d reveals the sun's successive rebounds

Greater concavity scatters rays into eight weak rebounds