An elementary treatise on geometrical optics / by R. S. Heath.

  • Heath, Robert Samuel.
Date:
1897
Catalogue details

Licence: Public Domain Mark

Credit: An elementary treatise on geometrical optics / by R. S. Heath. Source: Wellcome Collection.

Provider: This material has been provided by UCL Library Services. The original may be consulted at UCL (University College London)

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    EXAMPLES*. 1. The light from two sources is allowed to fall upon the same screen. One light is at a distance a and the light falls directly from it on the screen. From the other, which is at a distance 3a, the light falls at an obliquity of 60°. The illuminations of the screen from the two sources being equal, show that one source is 18 times as bright as the other. 2. A small white surface being placed horizontally on a table, and illuminated by a lamp or candle placed at a given horizontal distance a, show that the height of the flame from the table which will give the greatest possible illumination is equal to a/*/2. 3. If candles of equal brightness be placed at the angular points of a regular polygon, prove that a small plane area placed at the centre of the polygon will be equally bright on both sides, whatever be the orientation of its plane. 4. A small plane area is placed at right angles to the axis of a paraboloid of revolution whose convex surface is uniformly luminous. Prove that the illumination produced at the point of the plane where it meets the axis varies inversely as the distance of this point from the focus of the paraboloid. 5. A small plane area is placed parallel to a plane lamina of intrinsic brightness /, of breadth 2a, and of infinite length, at a distance c from the centre of the lamina in a line perpendicular to the lamina. Prove that the illumination at the centre of the plane area is TrccI/,J(a2 + c2). 6 The sides a of triangle are the bases of three infinite rect- angles of the same brightness, whose planes are perpendicular to the plane of the triangle ; show that all points within the triangle are equally illuminated. Find the position of a point in the plane of the triangle, such that the illuminations at that point received from the three rectangles may be equal. 7 A luminous point is placed on the axis of a truncated conical shell; prove that the whole illumination of the surface of the shell varies as o! c (C'2 + a'2)i'-(C2 + a2)i' where a, a' are the radii of the circular ends of the shell and c, e' the distances of the luminous point from their planes. 8 A right cone of vertical angle 26 is described about a given self luminous sphere, and at the points of the sphere in which the 2b ofthe cone cuts it, tangent planes are drawn ; prove that the ^an illumination of that part of the cone which is enclosed between these two planes varies as cos \Q cos 6.