从正侧面较远处俯瞰水碗中筷子的偏折角随筷子倾角及视角的变化

VARIATION OF THE DEFLECTION ANGLE OF CHOPSTICKS WITH THE INCLINING ANGLE AND THE ANGLE OF VIEW WHEN LOOKING DOWN AT THE WATER BOWL FROM FAR SIDE

文章首先介绍了从正侧面较远处俯看时,盛满水的碗中斜插筷子的虚像为一空间直线段,同时也介绍了水下物点的虚像点位置;然后计算出筷子虚像在竖直平面(Oyz平面)内的投影位置,以及所谓“主观意识”中筷子的偏折角∠CAD,进而将∠CAD在垂直于视线的平面内投影,从而得到人眼实际看到或相机拍到的筷子虚像的横向偏折角度,并在60°的视角下做了4次实验予以验证。根据理论结果,文章分别作出视觉中筷子的最大(或极大)偏折角及其倾角θ随视角r的变化曲线,以及几个典型的视角下偏折角随倾角的变化曲线;对筷子在特殊倾角、视角下的偏折角度分别进行讨论,指出一种奇异的突变现象。

This paper first introduces that the virtual image of the chopsticks inserted obliquely in a bowl full of water is a space straight line segment when it is viewed from far front side.At the same time,it also introduces the virtual image point position of underwater object.Then the projection position of the virtual image of chopsticks in the vertical plane(Oyz plane)and the deflection angle ∠CAD of chopsticks in the so-called“subjective consciousness”are calculated.And then,the ∠CAD is projected in the plane perpendicular to the line of sight,so as to obtain the transverse deflection angle of the virtual image of chopsticks seen by human eyes or photographed by camera.Four experiments are carried out to verify the results from the 60°angle of view.According to the theoretical results,the curves of the maximum(or extremal)deflection angle of chopsticks in vision and its inclination angle θ with the angle of view r are drawn respectively,and the curves of deflection angle with inclination angle under several typical visual angles are presented.The deflection angles of chopsticks under special inclination angle and angle of view are discussed respectively,and a strange mutation phenomenon is pointed out.