The field of view is the size of the
largest object that can be seen through an optical system by a detector that is
located at a fixed position. The size of the field can be expressed in units of
length (such as meters), although it is more convenient to use an angular
measure (e.g., degrees) in some situations.
For example, if you are looking at
your own image in a plane mirror, then both the object (your shoes, for
example) and the detector (your eye) are the same distance from the mirror. The
figure below shows that a ray of light can travel from your shoes (“S” in the
figure) to your eye (“E” in the figure) by striking a mirror (“M” in the
figure) that is considerably smaller than your own height. In fact, in order to
see your entire body at once, the mirror need be only one-half as tall as you
are. You can verify this by noting the symmetry of the figure or by using
simple plane geometry.
Although
the principles are unchanged, the detailed situation is somewhat more
complicated when the object and the detector are not at the same distance from
the mirror. For example, consider the field of view of the side mirror in a
car. Your eye (shown as “E”) can see any object whose rays fall within the area
bounded by the two rays that strike the edges of the mirror (shown as “M”) as
shown. Note that these two extreme rays have different angles of incidence and
therefore are not parallel to each other either before they strike the mirror
or afterwards.
Since
the two extreme rays are not parallel to each other, the field of view is a
pie-shaped region bounded by the two rays that are shown. This region can be
described either in terms of the wedge angle of the pie or in terms of its
width at some distance behind the car.
The
mirror in a typical car is about 16 cm wide (about 6.5 inches), and the
distance from your eye to the mirror is about 90 cm (35 inches). The field of
view of this configuration is a pie-shaped region where the wedge angle of the
pie is about 10 degrees. If we extend this pie-shaped region to just behind the
back of the car (about 25 feet or 7.5 meters behind the driver), the width of
the pie at that point is about 1.3 meters (about 4.5 feet). This pie-shaped
region can be moved by changing the position of the mirror, which changes the
angles of incidence of both rays simultaneously. However, the wedge angle of
the pie and the width of the region that can be viewed remains essentially
fixed, because these parameters are set by the width of the mirror and the
distance between the mirror and the driver’s eye, and these parameters do not
change when the mirror is tilted. The region that can be viewed is less than
the width of a typical lane on a roadway, so that this mirror will always have
a blind spot – a region where another vehicle might be located but which cannot
be seen by the driver. Rays emitted by objects in that region strike the
mirror, but they cannot reach the driver’s eye because there is no point on the
mirror where the angle of incidence of the ray produces a reflected ray which
is directed towards the driver’s eye.