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31. Whereabouts should a plane reflector be placed in that telescope, according to Newton's construction, so that the eye glass, of 1 inch focal length, may be set in the side of it?
32. What must be the ratio of refraction for yellow light, between air and water, supposing the radius of the arc of that colour in the secondary rainbow to be 52° 10′.
33. A plane mirror two feet in height is placed against a vertical wall, so that its lower edge is 4 ft. 2 in. from the ground. What part of his figure can a man 6 feet high see in it, when standing upright on the ground, supposing the vertical distance of the eyes from the crown of the head to be 116 of the whole height?
34. If parallel rays be incident on a sphere of a given refracting power, find that ray of which, when produced, the part included within the sphere, is to the analogous part of the refracted ray in a given ratio.
35. Given the distance of the points of incidence of two parallel rays on a transparent sphere, one of which passes through the center; required the distance between the points of emergence.
36. Given the apparent perpendicular depth of a fish under water; find the direction in which an arrow should be shot to hit it.
37. Let the surface of a plane reflector be always perpendicular to a line which revolves about one of its extremities, and cuts two other lines given in position; it is required to determine the focus of the reflector, so that an object moving in the intersection of the revolving line, with one of the given lines, the image shall move in its intersection with the other.
38. If a ray of light refracted into a sphere emerge from it after any given number of reflexions; determine the distance of the incident ray from the axis, when the arc of the circle intercepted between the axis and the point of emergence, is a minimum.
