What we know about our world relies
mainly on the surroundings having been perceived by ourselves or others using
our five senses. Among them, vision is the most important sense for
understating our world. Thus, visual perception lies at the root of most of our
empirical knowledge and is of great ontological and epistemological
significance.
Philosophy has a long history of
debating whether we perceive objects directly or indirectly, and whether we
perceive the mind-independent objects, the representations of these objects, or
simply the ideas in our minds. However, this paper is not going to tackle these
philosophical issues directly. The main concern of the paper is the
psychological aspect of visual perception, specifically to discern how we
perceive the objects’ sizes and what factors affect the way we perceive them.
Conventionally, the visual angle and optical geometry are used to explain and
calculate the retinal image’s size and to show the relationships between
retinal size, distance, and linear size of an object. Since the visual angle is
subtended and formed by two geometrical lines extending from two ends of an
object, the visual angle is a component of the geometrical model. The current
paper will provide enough evidence to prove that the new account of size
perception, manifested mainly by the perceived size equation, has more
explanatory and predictive power than the traditional account of the visual
angle and optical geometry.
The platform for the showdown between the traditional geometrical account and the new perceived size account are the plane mirrors and images in them. The topic of mirror images is usually found in the physics textbooks, not in the psychological literatures. However, mirrors and images in them provide a fertile field where the mechanism of size perception can be comprehensively investigated and ascertained, and the validity and reliability of the new perceived size equation can be empirically tested. The main purpose of investigating mirror images is not primarily about how the mirror images are formed per se, but also about the relationship between the mirror images and the mind, and about which approaches are more plausible in explaining and predicting mirror images, i.e., optical geometry or the perceived size equation.
The
geometrical diagram above shows how an image is traditionally believed to form
in a plane mirror. Two rays from the object point O that strike the mirror (M)
result in the two reflected rays which obey the law of reflection, i.e., that the
incident angle (θi) equals
the reflected angle (θr). The
image will be found where the reflected rays intersect, i.e., the image point I. Even though a plane mirror produces the
virtual image, meaning that light does not come from the image located behind
the mirror, the reflected rays that appear to come from the image are believed
to act just like the rays coming from the object itself. According to the
diagram above, the reflected rays always preserve the size and shape of the
object, so that the height of the object (H)
equals the height of the image (Hi);
and the distance between the mirror and the image point I (dim) is
always the same as the distance between the mirror and the object point O (dom),
i.e., H = Hi and dom = dim.
This
conventional description of mirror image formation based on optical geometry
reveals an implicit assumption that the mirror image exists just as much as any
other ordinary object, as far as our eyes are concerned, since an image can be
thought of as a collection of points all corresponding to a point on the
object, so that all the corresponding points on the image make a perfect
replica of the object. Hence, the mirror images are believed to have physical
existence, so much so that an image in the mirror is supposed to be able to
reflect again in a second mirror and then in a third mirror and so on, becoming
an image of an image of an image, etc. The present paper will effectively
challenge this assumption and claim, based on the mathematical calculations and
follow-up experiments, that the mirror images are mind-dependent. Furthermore,
because of the similarities between the perception of mirror images and that of
ordinary objects, it is postulated that the ordinary objects we perceive, like
the mirror images, might be the result of mental projections as well.
Since
the perceived size equation plays a pivotal role in the new account of size
perception, we are going to have a look at how this equation is derived first.