MOTION MOUNTAIN

200 4 images and the eye – optics
Challenge 196 e
Challenge 197 e
F I G U R E 149 The beauty of X-rays: X-ray images of a person (taken with a corpse) and of a sea shell
(© Nick Veasey).
X-ray imaging is so impressive that it has become a form of art. One of the foremost
X-rayartistsisNickVeasey,andtwoofhisworksareshowninFigure149.Amongmany
examples,hehaseven takenX-rayimagesofcompletebusesandaeroplanes.
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Lensesare important componentsin mostoptical systems.Approximately, thedistance
ofthelensfocusf,thedistanceoftheobjecttobeimagedo,andthedistanceofitsimage
iarerelatedbythethin lensformula
1
f =1 o +1 i . (81)
Itisnothardtodeduceitwiththehelpofraytracing.
If you ever are in the situation to design a lens, you will want to know the relation
between the shape of a lens and its focal distance. It turns out that there are two types
of lenses: The first type are spherical lenses which are easy and thus cheap to make, but
whose images are not perfect.The second lens type areaspherical lenses, which are hard
to fabricate, more expensive, but provide much better image quality. High-qualityoptical
systemsalwayscontainasphericallenses.
For historical reasons, most books on optics teach readers the approximate relation
between the geometric radii of a thin spherical lens, its refractive indexnand its focal
distance:
1
f =(n−1)(1 + 1 ) . (82)
R 1 R 2
This is called thelensmakerformula. Most aspherical lenses are approximately spherical,
so that the formula helps as a rough first estimate also in these cases.
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net