Bauhaus-Universität Weimar

Optic Projection: Principles, Installation and Use of the Magic Lantern, Projection Microscope, Reflecting Lantern, Moving Picture Machine
Gage, Henry Simon and Henry Phelps Gage
With the vertical lines in focus, add another convex cylinder of 
o-s diopter and arrange the axes of the two cylinders at right 
angles (cross the cylinders). All the lines will now be sharp, for 
the added convex cylinder increases the curvature where it was 
lacking, and thus gives the combination a symmetrical curvature. 
It is to be noted that when convex cylinders are crossed in this way 
they add to the original lens the dioptry of the cylinders. In this 
case 0.5 diopter, and the image is increased in size (fig. 389 C). 
Two concave cylinders can be used in the same way, but with 
concave cylinders the entire system is reduced in dioptry the 
amount of the cylinders. In this case it would reduce the dioptry 
half a diopter and hence the image would be smaller (fig. 
389 B). 
§ 930. Correction of astigmatism by the obliquity of the 
spectacles.—It was pointed out by Young (1800), that astigmatism 
might be corrected by making the spectacles sufficiently oblique to 
neutralize the defect. This can be demonstrated very strikingly 
as follows: 
Use the same outfit as in § 927. Make the image of the radial 
lines sharp on the screen and add the +0.5 diopter cylinder with 
the axis vertical (fig. 390). Now put a convex lens of 1 diopter in 
front of the cylinder and focus for the lines parallel to the axis of 
the cylinder (vertical in this case). Tip the convex lens up or 
down, i. e., across the axis of the cylinder, and when the right 
obliquity is reached the lines will all be sharp. This is because the 
tipped lens introduces the curvature lacking in the cylinder. This 
can be shown by removing the cylinder and the horizontal lines will 
be sharp showing that the vertical meridian is unchanged but the 
horizontal meridian has been increased in curvature. 
Use the same cylinder but a concave lens of 1 diopter instead 
of the convex lens ; focus the combination until the horizontal lines 
are sharp, then rotate the concave lens sidewise (i. e., parallel with 
the axis of the cylinder), and when at the right obliquity the radial 
lines will all be sharp. This is because the oblique, concave lens 
neutralizes the greater curvature of the +0.5 cylinder. In a word, 
the oblique position of the spectacle makes it act like a cylinder in


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