The above diagram shows an object O and an observer’s eye E in front of a plane mirror M and its image I behind the mirror, and all the relevant distances. Now we are going to assign definite values to these distances and relevant terms in the perceived size equation in order to calculate the perceived size, and conduct experiments to verify the calculations. The height of O is 20cm (i.e., H = 20cm). The distance between O and M is 50cm (i.e., d_om = 50cm). The distance between O and E is 50cm (i.e., d_oe = 50cm). The distance between E and M is 50cm. In addition, as mentioned earlier, d_i is the distance of the incident light from O to M and d_r is the distance of the reflected light from M to E. The length of d_i can be obtained by the formula:

Next, an experiment was conducted for the perceived image in the plane mirror according to the above diagram and the assigned values. The same book with 20cm in height was put at 50cm from a plane mirror. The observer’s eye was secured at a spot which was 50cm from the book and also 50cm from the mirror. A ruler was placed at 11.18cm from the eye and on the line of sight. The measurement of the book image, which is the perceived image height (P_ih), was 2cm in height as well. Thus, we know for sure that P_{ih =} P_h when the total distance, the actual height of the object and the measure-point are the same. By and large we perceive the images in the plane mirror the same as the ordinary objects in terms of the perception of their sizes.

Assuming d_om = d_im as believed by the conventional conception, the distance between E and I, which can also be called the distance of projection d_p (if the mental projection thesis were true), is calculated as below

If the principles that d_om = d_im, and O = I have been justified by sound observations and reasoning, then the perceived size equation is proven to be quite accurate since it is in good agreement with the principles. As long as these principles are correct, the perceived size equation is correct as well.

The conventional account of optical geometry assumes that there is a one-to-one relationship between O and I. This is also a commonsense understanding. When you look into a mirror, your image in it will stare right back at you. It seems that there is a direct connection between yourself and your image in the mirror. Every point of your image in the mirror can be conceived as connecting to each corresponding point on yourself with a straight and invisible line. The fact that O and I are directly across each other and have the same size and shape at the same distance from the mirror further confirms the belief that the mirror images are copied or reconstructed point by point along those point lines. This is the conventional account of mirror reflection.

However, the new account of size perception leads to a new conception of mirror reflection. The above calculations and experiments, i.e., P_{ih =} P_h and d_{p =} d_i + d_r, demonstrate that, rather than reflecting directly across the mirror, the mirror image could be the product of mental projection along the extended line of the reflected light. Our mind takes in information (which is the magnitudes of light intensity) from the photons entering the eye and forms brain images (B_i) based on the perceived size (P_s) of the mirror images as far as the size/shape perception is concerned. On the other hand, P_s of the mirror image is the outcome of mental projection of B_i. Without B_i, P_s of the mirror image cannot be projected out; likewise, without P_s, B_i cannot be formed. Hence, B_i and P_s are coexistent and interdependent. It is impossible for one to exist without the other, i.e., B_{i =} P_s. The formation of P_s and the projection of B_i of the mirror image occur simultaneously. It means that it takes no time for mirror images to appear. The mind assumes that the reflected light is the direction in which the light source has originated. The mind then projects B_i back to the source in accordance to the total distance of the incident and reflected light.

The mind must have a way to know the distance between the eye and the source besides knowing the intensity of the light, just like the planets in the Kepler’s third law which are aware of their exact distances from the Sun. The law states that the square of the orbital period of a planet is proportional to the cube of the mean distance from the Sun. Without the intrinsic knowledge of the mean distance from the Sun, it is unimaginable that the planets of different masses could orbit the Sun within a time frame precisely related to the distance.

It is nearly impossible to know how the mind and planets could ascertain the definite distances from other objects. But we can proffer a conjecture that the mind might rely on the photon disparity to determine distances from objects. Let’s assume that the photons A and B were perfectly close together when their journey started at the source; and they are certain magnitude apart after entering the eye. The mind may be able to quantify how much distance the photons A and B have traveled on the basis of the disparity of these two photons. Nevertheless, the distance information must have been built in the inverse-square law itself.

Based on the facts that d_{p =} d_i + d_r and O = I, we can speculate that the motivation for the mental projection is to restore the original object’s size/shape and location. The mind definitely has the precise information about the distances from objects no matter how it obtains them. The mind projects out B_{i /} P_s to a location that is exactly the same distance as that of the source to restore its actual size by the means of this formula: H = P_h· d/M_p, where the values of P_h, d, and M_p are all somehow known by the mind.

Besides whether this kind of motivation exists or not, it is obvious that the mirror image’s size is the same as the object’s size (i.e., H_i = H). More importantly, the distance between the mirror image and the eye is exactly the same distance from the eye to the object. This might be a strong evident to support the stance that mirror images are mental projections. On the other hand, the proponents of optical geometry may argue that the same distance from the mirror for both O and I and the equality of O and I also provide solid evidence to suggest that mirror image is an exact reconstruction of O behind the mirror. To uphold the mental projection notion, one can counter-argue that it is simply a geometrical coincedence that d_om = d_im, resulting from the mental projection with a purpose to return to the original location.

The optical and projected accounts are equally plausible thus far. It is a draw between these two different accounts regarding how the mirror images are formed, whether by light rays or by the mind. Neither side has the convincing evidence to prove the other side completely wrong. The tiebreaker will be offered later on in Case C.
       Notwithstanding, it is worth reiterating the view of the paper that the mirror image is not the representational image in the brain, but is the mental image projected out of the mind. The brain image and the perceived size are interchangeable and can both be regarded as percepts as far as the object’s size is concerned. The mirror image exists in the mind and at the same time also in the external world.