In Kaleidoscopes made of plates of glass, the last reflected image =β O ω=, Fig. 2, is more polarized than any of the rest, and is polarized in a plane perpendicular to =X E=, or in the same manner as if it had been reflected at the polarizing angle from a vertical plane parallel to =X E=. [Illustration: FIG. 20.] Let us now consider what will take place by a variation in the length of the reflecting planes, the angular extent of the field of view remaining always the same. If =A O E=, =A O Eʹ=, Fig. 20, be two reflecting plates of the same breadth =A O=, but of different lengths, it is manifest that the light which forms the direct sector must be incident nearer the perpendicular, or reflected at less obliquities in the short plate than in the long one, and, therefore, that a similarly situated point in the circular field of the shorter instrument, will have less intensity of light than a similarly situated point in a larger instrument. But in this case, the field of view in the short instrument is proportionally enlarged, so that the comparison between the two is incorrect. When the long and the short instrument have equal apparent apertures, which will be the case when the plates are =A O E=, =Aʹ O Eʹ=, then similarly situated points of the two fields will have exactly the same intensity of light. This will be better understood from Fig. 19, where =O E= may represent the long reflector and =Oʹ E= the short one. Then, if these two have exactly the same aperture, or a circular field of the same angular magnitude, the rays of light which flow from two given points, _p_, _n_, of the long instrument, will be reflected at a certain angle from the points =R=, _r_; but as the points _pʹ_, _nʹ_, are the corresponding points in the field of the shorter instrument, the rays which issue from them will be reflected at the same angles from the points =R=, _r_, the eye being in both cases placed at the same point _e_. Hence it is obvious, that the quantity of reflected light will in both cases be the same, and, therefore, that there is no peculiar advantage to be derived, in so far as the light of the field is concerned, by increasing the length of the reflectors, unless we raise the eye above _e_, till every part of the pupil receives the reflected rays.