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.