Background for Face Questions

This week we present one in a series of geometrical optics questions involving the image of the peculiar face below as produced by a variety of optical elements, such as different types of lenses and mirrors. Because there are a large number of them we will do a few at a time and present these problems on alternate weeks, mixed in with problems dealing with other topics.

This is a peculiar face, with no ears and only the tiniest lock of hair. No one wanted to call him "Dufus," so we will name him "Otto," because OTTO spelled out in block capital letters reflected in a mirror spells "OTTO."

Below are 28 different possible images of the face above, organized as seven sets of four. These image faces are available for a neat printout on two pages using ".pdf" files: click for Image Faces Page 1 or Image Faces Page 2. Alternatively, these files are available as ".htm" documents: Image Faces Page 1 HTML or Image Faces Page 2 HTML. The document Faces contains all of the faces.

Note that there are seven rows of faces, each of which contains images with four permutations of inversion: normal, inverted vertically, inverted horizontally, and inverted both horizontally and vertically. The seven sets of images show the "normal" face (a-d), the face magnified along both axes (e-h), the face demagnified along both axes (i-l), the face magnified along the vertical axis only (m-p), the face demagnified along the vertical axis only (q-t), the face magnified along the horizontal axis only (u-x), and the face demagnified along the horizontal axis only (y-bb). Note that there is a difference between image sets (m-p) and (y-bb), also between image sets (q-t) and (u-x).

Return to the question for this week by clicking on the "back" button to view the actual questions.

Possible Images

(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
(p)
(q)
(r)
(s)
(t)
(u)
(v)
(w)
(x)
(y)
(z)
(aa)
(bb)