Elements of Optics. Page 123. |
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B. Ill- DIOPTRICS. ,23
ting any incident ray RA, in G. Join DG, and draw Fig.
AF parallel to it, cutting the axis RD in F, then F y%.
is the focus. 74.
For RF : RD : : DF : DP ; that is, RF : RA : :
DF : AG, therefore the triangles RGD, RAF are
fimilar, and AF parallel to GD. And all rays
proceeding from G (or g) will emerge parallel to
GD.
Scholium.
In the firft Corol. we have a good practical
rule for finding the principal focus of a lens, having firft found any other focus by trial. And in
Cor. 2. we have another rule tending to the fame
purpofe, which finds the excefs of any other focal
diftance found by trial, above the principal focal
diftance. Both thefe are very eafy in practice.
PROP. XXIII.
The diftance of the radiating point and its focus, 7Z%
made by a convex lens, that is, RF is the leaft pof-
flble, when they are equidiftant from the lens.
For (by Cor. 2. Prop. XXI). RP : PD : : PD :
pF. Now if RP zzzpF, then the fum of the extremes RP, pF is equal to the fum of the means
2PD, which is conftant. But in any other cafe
CPropor. Prop. IX.) the fum of the extremes RP,
pF is greater than the fum of the means, that is,
greater than the fum of the extremes when they
are equal. And therefore RP -Fpf is the leaft
when RP zzpF, and adding Fp, the whole diftance RF is the leaft when RP rr^F, and confequently when RD rr DF.
Cor. The radiating point and its focus is at the
leaft diftance, from each other, when each of them is
diftant from the lens, twice the principal focal diftance.
For
| Title | Elements of optics. |
| Alternative Title | The elements of optics... / W. Emerson.;Perspective: or, The art of drawing the representations of all objects upon a plane. |
| Reference Title | Emerson, William, 1768. Elements of optics. |
| Creator | Emerson, William, 1701-1782. |
| Subject |
Optics -- Early works to 1800. Perspective. |
| Publisher | London, J. Nourse. |
| DateOriginal | 1768 |
| Format | JP2 |
| Extent | 21 cm. |
| Identifier | col147 |
| Call Number | QC353.E5 1768 |
| Language | English |
| Collection | Color and Optics |
| Data contributor | Linda Hall Library, LHL Digital Collections. |
| Title | Elements of Optics. Page 123. |
| Format | tiff |
| Identifier | col147151 |
| Rights | http://www.lindahall.org/imagerepro/terms/ |
| Type | image |
| OCR Transcript | B. Ill- DIOPTRICS. ,23 ting any incident ray RA, in G. Join DG, and draw Fig. AF parallel to it, cutting the axis RD in F, then F y%. is the focus. 74. For RF : RD : : DF : DP ; that is, RF : RA : : DF : AG, therefore the triangles RGD, RAF are fimilar, and AF parallel to GD. And all rays proceeding from G (or g) will emerge parallel to GD. Scholium. In the firft Corol. we have a good practical rule for finding the principal focus of a lens, having firft found any other focus by trial. And in Cor. 2. we have another rule tending to the fame purpofe, which finds the excefs of any other focal diftance found by trial, above the principal focal diftance. Both thefe are very eafy in practice. PROP. XXIII. The diftance of the radiating point and its focus, 7Z% made by a convex lens, that is, RF is the leaft pof- flble, when they are equidiftant from the lens. For (by Cor. 2. Prop. XXI). RP : PD : : PD : pF. Now if RP zzzpF, then the fum of the extremes RP, pF is equal to the fum of the means 2PD, which is conftant. But in any other cafe CPropor. Prop. IX.) the fum of the extremes RP, pF is greater than the fum of the means, that is, greater than the fum of the extremes when they are equal. And therefore RP -Fpf is the leaft when RP zzpF, and adding Fp, the whole diftance RF is the leaft when RP rr^F, and confequently when RD rr DF. Cor. The radiating point and its focus is at the leaft diftance, from each other, when each of them is diftant from the lens, twice the principal focal diftance. For |
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