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Journal for Geometry and Graphics 27 (2023), No. 1, 081--101
Copyright Heldermann Verlag 2023

Magnification Illusion - Change of Interpretation when Viewing Through a Telescope

Peeraya Sripian
Shibaura Institute of Technology, Tokyo, Japan

Takashi Ijiri
Shibaura Institute of Technology, Tokyo, Japan

Yasushi Yamaguchi
The University of Tokyo, Tokyo, Japan

When looking at a pair of parallel lines placed on a floor receding into the distance with a pair of binoculars, the parallel lines seem diverged instead of converged. This phenomenon has been reported as an illusion. We hypothesized that this perception is caused by the change in the three-dimensional interpretation of lines when a scene is magnified and named this perception the "Magnification Illusion". This might be similar to the change of optical slant angle interpretation, so the plane is more slanted to the fronto-parallel plane when magnified. In this work, we investigated the change due to magnification, such as the change in the interpretation of the perspective angle and the optical slant angle, and also tested with stimuli other than the parallel lines. The experiment result showed that the perspective angle is underestimated for all stimuli if magnified only when viewed with binocular vision. Meanwhile, the optical slant is underestimated even when viewed using the naked eye, and it is even more underestimated when magnified, regardless of binocular or monocular vision. In summary, this paper found that the change in the interpretation of perspective angles when magnified does occur in all pair of lines receding into the distance under binocular vision.

Keywords: Perception, linear perspective, slant perception, illusion.

MSC: 91E30; 62P15.

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