1904.] Lens- Systems, including Rotation of Images. 



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The same phenomena of rotation of the image on rotating the lens 

 system are observable in this case as in the cylindrical telescope, but 

 with this difference : the images, though sharply defined, are not 

 symmetrical, the object being magnified at right angles to the axis of 

 curvature, and not magnified parallel to it. 



The focal distance at which alone good definition is obtainable 

 is that at which the virtual image is the same distance from the eye 

 as the object. But to an astigmatic eye there are two distances at 

 which the instrument gives perfect definition, the direction of the 

 axis of curvature coinciding with the astigmatic axis of the eye in 

 one case and being at right angles to it in the other. 



The cylindrical telescope cannot by altering the focussing be made 

 to project an image on a screen like an ordinary telescope. To do 

 that we must employ two cylindrical telescopes with their axes 

 of curvature at right angles. They need not both be of the same 

 power, and, curiously enough, one may be situated inside the other 

 without interfering with its action. 



Polarised Light. 



Another peculiarity of the cylindrical telescope is rather remarkable 

 and extremely valuable. As would be expected, rotation of the tube 

 of a cylindrical telescope, though it rotates the image, is absolutely 

 without effect as regards the polarisation of the ray. There is, so 

 far as I know, no other means of rotating an image without altering 

 it in this respect, the ordinary erecting prism, whether silvered or 

 unsilvered, introducing a difference of phase. I have found the 

 cylindrical telescope extremely useful in some experiments where this 

 was important. 



Note added March 12. 



If the axis of a telescope of which the magnifying power is m is 

 moved sideways through an angle 0, the displacement of the image is 

 (1 ±m)0, taking the upper sign if the image is inverted, and the lower 

 sign if it is erect. 



In the telescope formed of two equal cylindrical lenses, parallel to 

 the axis of curvature m= -1, and at right angles to it m= +1. 

 Accordingly, if the axis of such a telescope is moved through an angle 

 in the plane of the axis of curvature, the displacement of the image 

 is zero. If it is moved in a plane at right angles to this the displace- 

 ment is 26. And if the plane of movement makes an angle of 45° with 

 the axis of curvature, the image appears to move at right angles to it. 

 The effect of rotating the telescope about its axis while moving it in 

 azimuth is very striking. 



A cylindrical telescope may be made with one lens as follows : — A 



