OPTICAL CENTRE. Every single lens has a certain point called its optical centre ; no such point, however, exists in the case of an achromatic lens, or combination of lenses. This should be distinctly understood, because ignorant persons frequently commit the blunder of speaking of the optical centre of a combination of lenses.
Confining our remarks, therefore, to the c,ase of the single lens.
If a ray of light, incident at any degree of obliquity upon a single lens, strikes it at such a spot as that the direction of the refracted ray within the glass, produced if necessary, passes through a certain point in the axis of the lens called the optical centre, the direction of the ray after emergence will be parallel to that at incidence.
This effect is brought about by the following circumstance :— A ray of light after refraction through a plate proceeds in a direc tion parallel to that which it had before. Now if the com.se of the ray within the glass when produced passes through the point called the optical centre, and we draw a tangent to the anterior surface of the lens at the point of incidence of the ray, and another tangent to the posterior surface of the lens at the point of emergence of the ray, we shall find that these two tangents are parallel, so that the lens for that particular ray may be considered as a plate, and the ray does not suffer deviation by being refracted through the lens, but merely displacement.
The position of the optical centre is constant, and independent of the obliquity of the incident ray ; so that in any whole pencil, no matter what its obliquity may be, which is incident upon the front surface of a lens, there is, provided that surface be large enough, a ptuticular ray, and only one, the direction of which after refraction passes through the optical centre.
The optical centre of a single lens is found thus :— If r be the radius of the front surface of a lens, the radius of the back surface, and t the thickness of the lens, then the distance of the optical c,entre, measured along the axis of the lens from the centre r t of the face of the front surface, is equal to The optical centre of a double convex lens is within the glass ;—of a plano-convex lens it is at the centre of the face of the back surface ;— and of a meniscus lens it is without the glass and behind it. By giving to r and 8 the proper algebraical sig,n, and a given magnitude, the position of the optical centre of any single lens may be readily found.
The use of the optical c,entre will be understood by referring to the figure on page 1. The focus, or circle of least confusion, of the pencil QAB is somewhere in the neighbourhood of c. Now the optical centre of the lens being within the glass the ray QC c passes through it, and may be considered as very approximately a straight line. If then we draw this line, and set off Cc equal to the focal length of the lens, we find the point c very approximately, and without going through the laborious investigation of the bent pencil QRF.
If, in this figure, AB were an achromatic lens, the point c would be found approximately by considering the lens as single, or homo geneous, and of the same external form.
In the case of a combination of lenses, this mode of proceeding evidently breaks down. A combination can neither have an optical centre, nor any point at all analogous to it.