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See also: Doublet

A doublet is the association of two lenses whose optical centers are S 1 and S 2, separated from a distance S 2  =  S 1 S 2.

Formulas

The point B has as an image the point Bi , which is used itself as object with the lens 2, which in fact a final image B I 2 The two basic formulas are:

ƒo/ X + ƒ I / xi = 1
said of Descartes, and that giving the growth
Γ  =  yi/there .
They can be written in the form:
x_i = \ frac {f_i \ cdot X} {(x-f_o)} and y_i= \ frac {f_i \ cdot there} {(x-f_o)}
These formulas make it possible to build the image Bi by the determination by the calculus of its coordinates xi and yi starting from the coordinates X and there of a point object B .

Principal points of a doublet

On the figure below, the object B is on a straight line parallel with the axis OX ( is constant there), which cuts the first lens in a point I . Its image B'1 is on the line IF'1 .

B , O1 and B'1 is aligned since the rays passing by O 1 are not deviated.

The point B'1 is used then as object with the second lens by using the same formulas with of course by taking as origin the X-coordinate O2 of the second lens; the final image B' is on the line JF' 2s where J is the intersection of IF' 1 with the second lens.

B' 1 , O 2 and B' 2 is aligned since the rays passing by O 2 are not deviated.

Remain to note that the place of the final image B' 2 is a line passing by F' , hearth image of the unit, and that this point F' is the image of the hearth image F' 1 of the first lens by the second lens, that is to say according to the formula of checking Newton:

F 2 F' 1 × F' 2 F' = ƒ2 × ƒ'2

Let us note in the passing that the hearth object F of the doublet has as an image by the first lens the hearth object F 2 of the second lens, which is written:

F 1 F × F' 1 F 2 = ƒ1 × ƒ'1

F 1 hearth object of the first lens has as an image by the whole of the doublet the hearth image of the second lens F' 2; this is written:

FF 1 × F' F' 2 = - ƒ1 · ƒ'1 · ƒ2 · ƒ'2/( F' 1 F 2) 2 = ƒ1 · ƒ2/ F' 1 F 2 × ƒ' 1 · ƒ'2/ F 2 F' 1

It is with these formulas that one can check the position of the points known as cardinal on the figure below.

Geometrical figures

Below an animation where in gray are represented the thin lenses. Animation shows, by geometrical construction:

  • in red: how to proceed to find the hearths and prnicipaux plans of the doublet.
  • then in blue: how to find the image B' finale by finding B' 1 initially product by L1 and which is used as object for L2.

Applications

See too

  • Optical

  • Mirror
  • geometrical lens
  • Stigmatisme
  • Optical
  • Diopter
  • Doublet half-wave (antenna)

Random links:Méréville (the Essonne) | Michiel Schapers | Othon Ier the Rich person | Roland the Clerk | Sorcerer' S Apprentice | 29