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9. A straight line is placed at the distance of 3 inches from a concave mirror of 9 inches radius: find the dimensions of the image.
10. Define the image of a portion of a parabola placed before a concave mirror, and having the center of the mirror for its focus.
11. There are three transparent plates A, B, C, bounded by plane surfaces. The ratio of refraction between A and B placed in contact is 43, and between A and C 78; what is it between B and C?
12. A ray of light falls at an angle of 45° on the plane surface of a refracting medium; the ratio of refraction is 32: what is the deviation?
13. What must be the refracting power of a transparent sphere in order that it may just collect parallel rays to a point within itself?
14. At what distance from a luminous point should a convex lens of two feet focal length be placed, in order that the focus of refracted rays may be at the same distance on the other side of it?
15. What equiradial lens is equivalent to a meniscus, the radii of which are 6 and 10 inches?
16. A double convex lens whose thickness is 3 inches and radii 30, and 20, is placed in air: what is its focal length?
17. What is the focal length of a lens composed of water contained between two meniscus-shaped watch-glasses, the radii of the surfaces being 5 and 7 inches, and the thickness supposed inconsiderable.
18. Supposing a diamond sphere to be just inclosed in a cube of glass, what would be the focus of rays incident perpendicularly at one of the points where the surfaces touch?
19. The caustic by refraction of a plane surface, for rays diverging from a point, is the evolute of an ellipse or an hyperbola, according as the passage is into a denser or a rarer medium.
20. What is the form of the caustic produced by a parabolic conoid of glass, the incident rays being all parallel to the axis.
