A Collection of Cambridge Mathematical Examination Papers Volume 2
John Martin Frederick Wright
Paperback
(RareBooksClub.com, March 6, 2012)
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1831 Excerpt: ...deviation in passing through one medium contained by parallel plane surface into another, as in passing immediately into the latter medium. 3. Given the focal length of a lens, which will just enable a short-sighted person to receive parallel rays, to determine the focal length of one, which will enable him to see to any given distance. 4. Rays tending to form an image at the point where the eye is placed, are received upon a concave lens, required to prove that the visual angle varies inversely as the square of the distance of the lens from the eye. 5. Given the focal length of a glass lens in air, find another, which, being compound with it, and the whole placed in water, the focal length shall equal that of the first in air. 6. When rays are incident parallel to the axis of a cycloid, to determine the form of the caustic and the law of the density. 7. Rays diverge from a point in the axis of double convex lens whose thickness equals one of its radii. Required the geometrical focus of refracted rays. 8. The image of a straight line perpendicular to the axis of a concave spherical reflector, and passing through its centre as seen by an eye placed in the axis at such a distance that all lines drawn to it from the reflector may be considered parallel, is determined by the equation y. (rยป + 2a;8) = 2xV('ยซ-xq). Investigate this, and trace the curve. 9. In the last question, find in what part of the reflector the.image of the diameter is formed. And explain clearly where the eye must be supposed to be placed when the image of a straight line formed by a spherical reflector is said to be a conic section. 10. An homogeneous pencil of parallel rays is incident on a sphere of refracting substance, so as to emerge parallel after (p) internal reflections; r...