达式，并作出在多种典型的观察情形下筷子虚像的三维曲线图; 指出当人眼从侧面观察时，即使在视觉上筷子的虚像也应是

曲线; 在迎面和垂直侧面，将30 cm 视距与∞远视距俯视观察到的筷子虚像进行比较，指出当视角在60°附近时两者的差异最

大; 计算并作出迎面和垂直侧面30 cm 视距俯视时左、右眼分别看到的筷子虚像，指出两者的差异均随视角的增大而增大.

文末对本文筷子虚像点坐标表达式的由来进行了解释，指出该解析结果的优势所在.

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.