本文介绍抛物线的一个光学性质的3种证法.设F是抛物线的焦点,M是抛物线上任意一点(如图1),MT是抛物线在点M处的切线,MN是法线,ME是平行于抛物线的轴的直线,那么法线MN必平分∠FME,即φ1=φ2.图1证法1取坐标系如图1,这时抛物线方程y2=2px.设点M的坐标为(x0,y0),则法线MN的方程是 This article describes three proofs of an optical property of a parabola. Let F be the focus of the parabola, M be any point on the parabola (Fig. 1), MT be the tangent of the parabola at point M, MN be the normal, ME be parallel For the straight line of the parabola axis, then the normal MN must be evenly divided FME, that is φ1 = φ2. Figure 1 Proof 1 Take the coordinate system as shown in Figure 1, then the parabola equation y2 = 2px. Set the coordinates of the point M to (x0, Y0), the normal MN equation is