Abstract: Based on the existing optical knowledge，this paper deduces the coordinate expression of virtual image

points of chopsticks inserted obliquely at 30 degrees into the bowl full of water when one looks down from the

front and side. The three-dimensional curves of virtual image of chopsticks under various typical observation situations

are drew. It is pointed out that when one observes from the side，the virtual image of chopsticks should be a

curve even in the sense of sight. The virtual images of chopsticks observed at 30 cm visual distance and ∞ far visual

distance are compared when one looks down from the front and vertical side，the difference between them is greatest

when the angle of view is near 60 degrees. The virtual images of chopsticks seen by the left and right eyes at 30 cm

visual distance overlooking from the front and vertical sides are calculated and made，the difference between the two

images increases with the increase of visual angle. Finally，the origin of the coordinate expression of virtual image

points of chopsticks is explained，and the advantages of the analytical results are pointed out.

Key words: chopsticks, virtual image, coordinates, angle of view, visual distance