A Treatise On Optics

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55. is a luminous point situated on AB the diameter (2r-) of a hollow sphere (centre 0) polished at A and 5:/ and /' are the foci of the pencils reflected at A and B respectively — shew that 4 //' = • 4" 56. Explain the principle of the Kaleidoscope: — and shew that when the mirrors are inclined at 60°, the area of the field of view is to the area of the transverse section of the tube as 27r -I- 3 \JZ : ir.
57. The locus of the image of a luminous point reflected in a plane mirror is a c
...ircle, prove that the mirror always touches a conic section.
58. The radii of the centre and inner surfaces of a spherical refracting shell are R, r respectively. Prove that the distance from the centre of the geometrical focus of a pencil of parallel rays after refraction through the whole shell is 1 II Rr 2fj,-lE-r' 264 EXAMPLES AND PEOBLEMS.
59. A ray emanates from a luminous point P and after two reflexions at a reflecting circle returns to the point again, shew that P +

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