Polarisation, analyser chains and phase
GRE Subject Test · GRE Physics Topic 31 6:15 English narration · English + 中文 subtitles burned in
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Putting a third polariser between two crossed ones can let light through, although every filter only removes energy.
在两片正交的偏振片之间插入第三片偏振片，可以让光透过，尽管每片偏振片都只会去掉能量。
This topic follows intensity through a chain of analysers, uses relative phase to tell linear, circular and elliptical light apart, and applies Brewster's angle.
本主题追踪光强通过一串检偏器的变化，用相对相位区分线偏振、圆偏振和椭圆偏振光，并应用布儒斯特角。
For propagation along z, a transverse electric field can have x and y components.
沿 z 方向传播时，横向电场可以有 x 和 y 分量。
Linear polarisation means the field oscillates along one fixed line; an ideal analyser transmits the projection along its axis.
线偏振意味着电场沿一条固定直线振动；理想检偏器透射电场在其透振方向上的投影。
The field amplitude becomes E cosine theta, so the intensity becomes I cosine squared theta.
电场振幅变为 E cos θ，因此光强变为 I 乘以 cos θ 的平方。
Here theta is between the incoming polarisation and that analyser, and I is the intensity immediately before it.
这里 θ 是入射偏振方向与该检偏器之间的夹角，I 是紧挨在它之前的光强。
An unpolarised beam is a statistical mixture of transverse orientations; an ideal first polariser passes half its mean intensity.
非偏振光是各种横向取向的统计混合；理想的第一个偏振片透过其平均光强的一半。
The outgoing beam is then linearly polarised along the filter axis.
出射光随后沿偏振片透振方向线偏振。
Do not apply a new factor of one half at every later filter, or use one angle to the original source for the whole chain.
不要在后面每个偏振片处都再乘二分之一，也不要对整条链只用相对于原光源的一个角度。
After each analyser, update both the intensity and the polarisation direction.
每经过一个检偏器，都要同时更新光强和偏振方向。
For an initially unpolarised beam and ideal axes alpha 1, alpha 2 and alpha 3, the final intensity is I nought over 2, times cosine squared of alpha 2 minus alpha 1, times cosine squared of alpha 3 minus alpha 2.
对于初始非偏振光和理想透振方向 α1、α2、α3，最终光强等于 I0 除以 2，乘以 α2 减 α1 的余弦平方，再乘以 α3 减 α2 的余弦平方。
Two crossed filters transmit zero in this model; a middle oblique axis changes the direction before the final projection.
在此模型中，两个正交偏振片的透射为零；中间一个斜向透振方向会在最后投影之前改变偏振方向。
This increase relative to the crossed pair does not create energy; every step still has transmission between zero and one.
相对于正交的一对偏振片，这种增加并没有创造能量：每一步的透射率仍在零和一之间。
Real filters have absorption, imperfect extinction and wavelength dependence.
实际偏振片有吸收、消光不完全以及波长依赖。
Use the ideal law only when those losses are excluded or separately specified.
只有在排除或另行说明这些损耗时才使用理想定律。
Write E sub x equals A cos omega t and E sub y equals B cos open parenthesis omega t plus delta close parenthesis at a fixed point.
在固定点写出 Ex = A cos ωt 和 Ey = B cos(ωt + δ)。
Equal or opposite phases give a line, including a line at an oblique angle. Equal nonzero amplitudes and a quarter-cycle phase difference give a circle.
同相或反相产生直线，包括斜线；等幅非零振幅与四分之一周期相位差产生圆。
Unequal amplitudes at quarter-cycle phase give an ellipse.
四分之一周期相位差下不等幅产生椭圆。
A quarter-wave plate adds a relative phase of pi over 2 between its principal axes under its design conditions.
四分之一波片在其设计条件下于主光轴间引入 π/2 的相对相位。
A linear input at 45 degrees supplies equal components, so the outgoing field can be circular.
45° 线性输入提供等量分量，因此出射场可为圆偏振。
A linear input along a principal axis has only one component and remains linear.
沿主光轴的线性输入仅含一个分量，保持线性。
For circular input, every ideal linear analyser passes half the intensity.
对于圆偏振输入，每个理想线性检偏器透过一半强度。
Handedness requires a declared viewing direction and phase convention.
旋向性需声明观察方向与相位约定。
For incidence from a transparent nonmagnetic medium with refractive index n sub 1 into a medium with refractive index n sub 2, Brewster's angle measured from the normal satisfies tangent of theta sub B equals n sub 2 divided by n sub 1.
当光从折射率为 n₁ 的透明非磁性介质入射到折射率为 n₂ 的介质时，相对于法线测量的布儒斯特角满足 tan θ_B = n₂/n₁。
At that angle, the reflected p component, whose electric field lies in the plane of incidence, vanishes in the ideal dielectric model.
在该角度下，电场位于入射面内的反射 p 分量在理想电介质模型中消失。
Reflected light from unpolarised input is then s polarised, perpendicular to that plane.
来自非偏振输入的反射光变为 s 偏振，垂直于该入射面。
Snell's law gives a refracted angle complementary to theta sub B.
斯涅尔定律给出的折射角与 θ_B 互余。
This is distinct from the critical-angle condition sine of theta sub c equals n sub 2 divided by n sub 1, which requires n sub 1 greater than n sub 2 and concerns total internal reflection.
这与临界角条件 sin θ_c = n₂/n₁ 不同，后者要求 n₁ > n₂，且涉及全内反射。
Brewster reflection does not imply that the entire incident intensity is reflected or that the transmitted beam is completely polarised.
布儒斯特反射并不意味着全部入射强度被反射，也不意味着透射光束完全偏振。
Unpolarised light of intensity I naught meets axes at 0, 30 and 90 degrees.
强度为 I0 的非偏振光依次通过轴向为 0°、30° 和 90° 的偏振片。
The first filter passes half.
第一片透过一半。
Each later filter uses the angle from the axis just before it: 30 degrees, then 60.
之后每一片都用与前一片轴的夹角：先是 30°，再是 60°。
So the output is one half times cos squared 30 times cos squared 60: three thirty-seconds of I naught, not the zero that the first and last axes alone would predict.
所以输出等于二分之一乘 cos² 30° 乘 cos² 60°：I0 的三十二分之三，而不是只看第一片和最后一片时预测的零。
Insert one ideal analyser at angle theta between two crossed ideal polarisers.
在两个正交的理想偏振片之间插入一个与入射光成theta角度的理想检偏器。
Derive final intensity for unpolarised input I zero and find the angle giving maximum output.
推导非偏振光I零作为输入时的最终光强，并求出使输出最大的角度。
Compare with removing the middle analyser.
将其与移除中间检偏器的情况进行比较。
I sub f equals I sub 0 divided by 2, times cosine squared theta, times sine squared theta.
I_f 等于 I_0 除以 2，乘以 cos²θ，再乘以 sin²θ。
This is equal to I sub 0 divided by 8, times sine squared of 2 theta.
这等于 I_0 除以 8，乘以 sin²(2θ)。
The maximum is I sub 0 divided by 8 at 45 degrees between the outer axes, modulo equivalent axes.
最大值为 I_0/8，出现在外轴之间夹角为 45 度时（考虑等效轴）。
Removing the middle analyser gives zero.
移除中间检偏器后输出为零。
It changes polarisation while reducing intensity; it does not create energy.
它改变了偏振态的同时降低了光强；但它不会创造能量。
Award chain, identity, optimum and comparison slash interpretation.
评分点包括：链式推导、恒等式、极值条件以及比较与解释。
Malus intensity uses cosine squared of the angle to the immediately preceding polarisation; a phase plate changes relative phase, while a polariser removes a field component.
马吕斯定律中的光强使用与前一偏振态夹角余弦的平方。 相位板改变相对相位，而偏振片则会移除一个场分量。
Malus's law: Ideal linear analyser intensity law, I sub out equals I sub in times cosine squared of theta, for linearly polarised input.
马吕斯定律：理想线偏振分析器强度定律，I下标out等于I下标in乘以cos²θ，适用于线偏振入射光。
Brewster angle: Incidence angle at which the reflected p component vanishes for the ideal dielectric interface.
布儒斯特角：对于理想电介质界面，反射p分量消失时的入射角。
Retrieve the meanings without reading the definitions, then change a parameter in the original transfer and test the limiting case.
在不阅读定义的情况下回忆含义，然后改变原始传递中的一个参数并检验极限情况。