5.双折射 Double refraction 1)双折射现象e-光 calcite O光 方解石 藏新谢 unpolarizedhlight 自然光 The“ double- bending?” of a beam transmitted through calcite, is called double refraction 2) the ordinary ray(O-ray) and the extraordinary ray(e-ray).(1687年惠更斯研究) a) two beams are polarized light with their planes of vibration at right angles to each other
5. 双折射 Double Refraction 1) 双折射现象 unpolarized light 自然光 O光 e-光 双折射 双折射 calcite 方解石 The “double-bending” of a beam transmitted through calcite, is called double refraction. 2）the ordinary ray (O-ray) and the extraordinary ray (e-ray).（1687年惠更斯研究） a）two beams are polarized light with their planes of vibration at right angles to each other
b)O-ray obey the refraction law The crystal has a single index 光 of refraction n O光 c) The e-ray index of refraction varies with irection from no然光 方解石 to a smaller value (for calcite)n sn sin i C 为什么S/1 e光在晶体中传播, 光速是一变值。 对e光:snte=n12(∠i)≠COn(与入射角有关 SIn 且不为定值)
n const r i = o = 0 0 sin sin O光 e光 b）O-ray obey the refraction law. The crystal has a single index of refraction no . c）The e –ray index of refraction varies with direction from no to a smaller value (for calcite) ne . n i const r i e e e = ( ) sin sin （与入射角有关 且不为定值） 对O光： 对e光： （与入射角无关 且为定值） e光在晶体中传播， 光速是一变值。 n v C r i = = sin sin 为什么？ 自然光 方解石
3) optic axis光轴 a) optic axis光轴-- The direction at which a 78 68° beam transmitted through calcite without double 10 refraction called optic axis b) The optic axis is found by erecting a line at 78 either of the two corners 光轴 where three obtuse angles met(tte“ blunt” corners), making equal angles 680 with the crystal edges. Any line in the crystal parallel to this line is also an optic axis
3）optic axis 光轴 78º 78º 68º 102º a）optic axis 光轴--- 光轴 The direction at which a beam transmitted through calcite without double refraction called optic axis. b) The optic axis is found by erecting a line at either of the two corners where three obtuse angles meet (the “blunt ” corners), making equal angles 68ºwith the crystal edges. Any line in the crystal parallel to this line is also an optic axis
) principal section主截面 78 The principal section is consist of the normal to crystal surface and optic axIS。 注意: 78° OAny section in the crystal parallel to this section is 光轴 also the principal section @when incident ray lie in the principal section, the vibration of o-ray normal to the principal section and the vibration of e-ray parallel to the principal section
光轴 4）principal section 主截面 The principal section is consist of the normal to crystal surface and optic axis. Any section in the crystal parallel to this section is also the principal section. 注意： when incident ray lie in the principal section, the vibration of O-ray normal to the principal section and the vibration of e-ray parallel to the principal section. n+ ˆ 102º 78º 78º
②入射面在主截面内时,0光e光的振动面互相垂直 Two planes of vibration at right angles to each other 且o光为振动面垂直 78 于主截面的偏振光; e光为振动面平行于 主截面的偏振光; 5)正晶体与负晶体 78° 光轴 Positive crystal and negative crystal Positive crystal: ne>n, Negative crystal:ne也可也可<v
78º 光轴 入射面在主截面内时，o光e光的振动面互相垂直 Two planes of vibration at right angles to each other. 且o光为振动面垂直 于主截面的偏振光； e光为振动面平行于 主截面的偏振光； n+ ˆ 5）正晶体与负晶体 Positive crystal and negative crystal ne 可以也可 no Negative crystal: ne no 78º
6)用惠更斯原理解释双折射现象 因O光沿各向传播的速度是相同的,故O光的波面是球面。 而e光在晶体内沿各向传播的 速度不相同,所以e光的波面 781 是椭球面。 正晶体-v0>v 负晶体-v< 光轴 光轴 78° e光 在晶体内一个点波 0光 源发光的波阵面: 负晶体 正晶体
78º n+ ˆ 6）用惠更斯原理解释双折射现象 e v v 0 因O光沿各向传播的速度是相同的，故O光的波面是球面。 而e光在晶体内沿各向传播的 速度不相同，所以e光的波面 是椭球面。 正晶体-- 负晶体-- e v v 0 在晶体内一个点波 源发光的波阵面： 78º 光轴 负晶体 正晶体 o光 e光 光轴
incident ray lie in the principal section:(负晶体) A There is a angle between optic axis and crystal surface 光轴与晶体表面有一夹角(正入射) 自然光士 optic axis 光輛
incident ray lie in the principal section：（负晶体） A）There is a angle between optic axis and crystal surface 光轴与晶体表面有一夹角（正入射 ) 自然光 optic axis 光轴
b) optic axis is parallel to the crystal surface 光轴与晶体表面平行(正入射) 自然光 结论:V0≠vn0≠n有双折射 光轴 光 光 Oe二光通过厚度d的光程差:=(mn-mn)d 6=2/4 6=2/2 四分之一波片二分之一波片(半波片)
B） optic axis is parallel to the crystal surface 光轴与晶体表面平行（正入射） 自然光 o光 e光 光轴 O e 二光通过厚度d的光程差： = (ne − no )d = / 4 = / 2 四分之一波片 二分之一波片（半波片） 结论： e v v 0 n0 ne 有双折射
C)optic axis is normal to the crystal surface 光轴扫晶体表面垂值(正入射 主自然光主 光轴 光 e光 无双折射现象 (负晶体)
自然光 o光 e光 光轴 C） optic axis is normal to the crystal surface 光轴与晶体表面垂直（正入射） 无双折射现象 （负晶体）
D) There is a angle between optic axis and crysta face 光轴与晶体表面有一夹角(斜入射) 光轴 光轴 晶体 e光
o光 e光 晶体 光轴 光轴 D) There is a angle between optic axis and crystal surface 光轴与晶体表面有一夹角（斜入射）