Page:Harold Dennis Taylor - A System of Applied Optics.djvu/29

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SECT.I
A RECAPITULATION
7

The radius of curvature A..C is to be considered as an intrinsically positive quantity whether the surface be convex or concave; and then—

For concave reflector—


If rays of the incident pencil are divergent, then Q..A is positive.Reflector Conventions as to signs
If rays of incident pencil are convergent, then A..Q is negative.
If rays of reflected pencil are convergent, then A..q is positive.


If rays of reflected pencil are divergent, then q..A is negative.
And for convex reflector—


If rays of incident pencil are convergent, then A..Q is positive.
If rays of incident pencil are divergent, then Q..A is negative.
If rays of reflected pencil are divergent, then q..A is positive.


If rays of reflected pencil are convergent, then A..q is negative.

Instances of applications of signs to reflected pencils.For instance, in the case of Fig.2d we have , but by convention A..Q is a negative quantity, therefore the formula is or , therefore A..Q comes out divergent and positive.

Should Q..A or A..Q be infinite or the rays of the incident pencil be parallel, then of course becomes zero, and becomes or , and the rays converge to or diverge from the principal focus of the mirror.

The dotted lines in the figures indicate negative distances, and the full lines the positive distances.

Plane Refracting Surfaces

In the case of normal or perpendicular incidence of small pencils at a plane refracting refractive indexsurface bounding a transparent substance whose refractive index = μ, while that of the left-hand medium = o, the simple relationship A..q=μ(A..Q) holds good. See Figs.3a and 3b.

Spherical Refracting Surfaces

In the case of direct refraction of normal pencils by spherical surfaces, as in Figs. 4a, b, c, d, e, f, g, and h, the formula

Formula connecting focal distances in case of refraction at single surface.
or
II.