404
LIGHT.
Light
Simplest, orHersc‘))elianconstruc-tion.
391.
Newtonian
construe-
turn.
393.
Cassegraiu-
ian.
394 .
but as such telescopes are only used of a great size, and for the purpose of viewing very faint celestial objects,in which the light diffused by aberration is insensible, little or no inconvenience is found to arise from this cause.Such is the construction of the telescopes used by Sir William Herschel in his sweeps of the heavens.
To obviate the inconvenience of the stoppage of rays by the head, Newton, the inventor of reflecting tele-scopes, employed a small mirror, placed obliquely, as in fig. 83, opposite the centre of the large one. Thusparallel rays PA, PB, emanating from a point in the axis of the telescope, are received, before their meeting, ona plane mirror C D inclined at 45° to the axis, and thence reflected through a tube projecting from the side ofthe telescope to the lens G, and by it refracted to the eye E. It is manifest, that if the image formed by themirror A B behind C D be regarded as an object, an image equal and similar to it (Art. 335) will be formedat F, at an equal distance from the plane mirror; and this image will be seen through the glass G, just as if itwere formed by an object-glass of the same focal length placed in the prolongation of the axis of the eye-tube,beyond the small mirror, (supposed away.) Hence the same propositions and formulae will hold good in theNewtonian telescope, as in the astronomical and Galitean, for the magnifying power, field of view, and positionof the eye, substituting only 2 R for L, and 2 R — D for L — D, and recollecting that R is negative, as themirror has its concavity turned towards the light.
The Gregorian telescope, instead of a small plain mirror turned obliquely, has a small convex mirror with itsconcavity turned towards that of the large one, as in fig. 84 ; but instead of being placed at a distance from thelarge one equal to the sum of the focal lengths, the distance is somewhat greater; hence the image p q, formedin the focus of the great mirror, being at a distance from the vertex of the small one greater than its focal length,another image is formed at a distance, viz. at or near the surface of the great mirror, at r s. In the centre of thelarge mirror there is a hole which lets pass the rays to an eye-lens g. The adjustment to parallel or divergingrays, or for imperfect eyes, is performed by an alteration of the distance between the mirrors made by a screw.
The Cassegrainian construction differs in no respect from the Gregorian , except that the small mirror is convexand receives the rays before their convergence to form an image. The magnitude of the field, the distance of theeye and of the mirrors from each other, are easily expressed in these constructions; the latter being derived fromthe former by a mere change of sign in the curvature of the small mirror. Let then R' and R" be the curvaturesof the two mirrors, then in the Gregorian telescope IV is negative and R/' positive ; and if we put t for thedistance between their surfaces, (t being negative, because the second reflecting surface lies towards the incidentlight) we shall have for an object whose proximity is D
f
IV = D ; /' = 2R'-D'=2R ;
adopting the formula and notation of Art. 251.
-D; f" = 2 R" — D";Now these give, by substitution,
D" -
1 -/' t' ’
D'
2R'-D
/" = 2 R" -
2R'-D
1 - t (2 R' - D) ’ " ” 1 - t (2 IV - D)
_ 2 R" - 2 R' + D - 2 t (2 R' - D) . R"
— 1 — t (2 1V — D) ’
(/)
This is the reciprocal distance of the second image from the second reflecting surface. If we wish that the imageto be viewed by the eye-lens should fall just on the surface of the large mirror, we have only to put f" =
(because f n is positive, and t negative.) For parallel rays this gives
- t
Or)
R' R" . <* + (4 R' — 2 R'O t — 1 = o;
whence t may be found when IV and R" are given, or vice versa.
The description of other optical instruments, and of the more refined construction of telescopes, &c. must bedeferred till we are farther advanced in our account of the physical properties of light, and especially of thedifferent refrangibility of its rays and their colours, which will form the object of the next part.