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21. A small rectilinear object is placed before a double convex lens, of inconsiderable thickness, inclined to the axis at an angle of 30°, and the distance of its intersection with the axis from the lens, is four times the focal length; shew that the image is an arc of an ellipse, and find the axis major of it.
22. If an object be placed in the principal focus of a convex lens, the visual angle is the same, whatever be the place of the eye on the axis.
23. In a convex lens with surfaces of equal curvature, the spherical aberration exceeds the chromatic, if the semi-aperture be greater than 19 of the radius.
24. If the dispersive powers of two prisms be inversely as their refracting angles, they will form an achromatic compound prism, when placed against each other in opposite directions.
25. It is required to achromatize a double concave lens of rock crystal, by means of a meniscus of iceland spar, which is just to fit into it. What must be the radius of the inner surface of the meniscus, supposing those of the concave lens to be each 5 inches, the refracting powers of the substances being 1.547, and 1.657?
26. How many times will the surface of a minute object be magnified by a globule of spirit of wine 140th of an inch in diameter, supposing the least distance of correct vision to be 5 inches?
27. What must be the limit of the angular distance of two stars, that they may be both seen at once through an Astronomical telescope 4 feet long which magnifies 47 times?
28. Compare the fields of view of an Astronomical and a Galilean telescope, supposing the object glasses to be each 4 inches in diameter, and of 3 feet focal length, and the eye glasses of 14 inch aperture, and 1 inch focal length.
29. How much must the Galilean telescope, mentioned in the last question, be lengthened, to be used as a microscope, supposing that the object to be examined would be placed at 3 ft. 2 in. from the object glass?
30. What is the focal length of the eye-glass of Sir W. Herschel's great telescope? See page 131, Note.
