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Figure 2.14
A set of light rays is emitted from the tip of the glamorous movie star’s nose on the film, and reunited to form a spot on the screen which is the image of the same point on his nose. The
distances have been distorted for clarity. The distance y represents the entire length of the theater from front to back.
In a movie theater, the image on the screen is formed by a lens in the projector, and originates from one of the frames on the strip of celluloid film (or, in the newer digital projection
systems, from a liquid crystal chip). Let the distance from the film to the lens be
, and let the distance from the lens to the screen be
. The projectionist needs to adjust
so that it is properly matched with
, or else the image will be
out of focus. There is therefore a fixed relationship between
and
, and this relationship is of the form







where
is a property of the lens, called its focal length. A stronger lens has a shorter focal length. Since the theater is large, and
the projector is relatively small,
is much less than
. We can see from the equation that if
is sufficiently
large, the left-hand side of the equation is dominated by the
term, and we have
. Since the
term doesn't completely vanish, we must have
slightly greater than
, so that
the
term is slightly less than
. Let
, and approximate
as being infinitesimally small. Find a simple expression for
in terms
of
and
.
















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