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MISCELLANEOUS QUESTIONS.
1. A luminous point is placed at the distance of 5 feet from a concave mirror of one foot radius; to what point will the rays be reflected?
2. In the above instance, determine the initial velocity of the focus, supposing the luminous point to advance towards the mirror at the ratio of 2 feet per second.
3. Supposing two rays inclined to each other at an angle of one degree to fall nearly perpendicularly on a convex mirror of which the radius is 5 feet, placed at 312 feet from the point of intersection of the rays; what will be their mutual inclination after reflexion?
4. A light is placed behind a screen, at the distance of two inches from a concave reflector of 9 inches principal focal length; whence do the rays appear to proceed?
5. What is the extreme aberration when rays diverging from a point fall perpendicularly on a convex mirror of 3 inches diameter, and 10 inches focal length, at the distance of 30 feet?
6. Supposing the focal length and aperture to be the same, which gives the greater aberration, a concave mirror or a convex one?
7. A concave mirror being formed by the revolution of an ellipse (whose axes are 3 and 2 feet), about the axis major, to what point will those rays be reflected which diverging from the centre of the figure, fall on the circle whose diameter is the latus rectum?
8. A small object is placed between two plane mirrors inclined to each other, so that a perpendicular drawn from the object to their intersection makes an angle of 3° with one, and of 12° with the other: what is the number of images formed?
