Focus and Optics 
To FIND THE FocaL LENGTH oF A LENS.—Many methods 
have been suggested for finding the focal length, equivalent 
focus, or focus of a lens, and many of them require a knowl- 
edge of the position of the nodal point of emergence. This 
can be found by calculation, but it can also be determined by 
temporarily mounting the lens in a V-shaped groove on a 
small block of wood, so that the lens can be moved to and fro. 
Or take a large flat cork and drive a nail through the center, 
so that the cork will turn on this as an axis. Fasten the lens 
to the cork by a rubber band, and focus some very distant 
object, such as the sun or moon, on a piece of card or ground 
glass also temporarily held on a cork. When the image is 
quite sharp, rotate the lens, and, if the image moves, the nodal 
point of emergence of the lens is not over the point of rota- 
tion of the cork. The lens should be shifted to and fro and 
the image again focussed until it no longer moves with the 
rotation of the lens. Then the node of emergence is exactly 
over the axis of rotation, and this is the point from which the 
focal length should be measured. 
The following method is accurate and calls for measure- 
ments which are easily made. Focus a foot rule to a definite 
size, measure the distance between the rule and the image, and 
call this D. Then focus to a larger size, again measure the 
distance as before, and call this d. Then the following © 
formula will give the focus: 
d—D 
( at) R*+1 
r vie 
R being the ratio of image to object in the first case, and r 
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