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GRE Subject Test · GRE Physics หัวข้อ 33 6:38 การบรรยายภาษาอังกฤษ · คำบรรยายภาษาอังกฤษ + 中文 ลอยตัวบนภาพ
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Transcript
A negative image distance is not a failed calculation to fix with an absolute value: it locates a virtual image.
负的像距并不是需要用绝对值修正的错误结果：它确定了一个虚像的位置。
This topic places thin-lens and mirror images with one declared sign convention, reads orientation from the signed magnification, and passes each image to the next element as its object.
本主题用一个明确声明的符号约定确定薄透镜和面镜的成像位置，从带符号的放大率判断像的正倒，并把每个像作为下一个元件的物。
Use the real-is-positive convention for this unit.
本单元采用“实为正”约定。
A real object sends diverging incident rays into the element, so s is positive; an already converging incident beam can represent a virtual object, with s negative.
实物向光学元件发出发散的入射光，因此 s 为正；已经会聚的入射光束可以代表虚物，此时 s 为负。
A real image has s prime positive, while a virtual image has s prime negative.
实像的 s 撇为正，虚像的 s 撇为负。
The paraxial equation is 1 over f equals 1 over s plus 1 over s prime, and the transverse magnification is M equals minus s prime over s.
近轴方程为 f 分之一等于 s 分之一加 s 撇分之一，横向放大率 M 等于负的 s 撇除以 s。
A converging lens has f positive and a diverging lens f negative.
会聚透镜 f 为正，发散透镜 f 为负。
For left-to-right light and a real object at negative x relative to a lens at x equals zero, a real image lies at x equals s prime, which is positive; a negative s prime puts its virtual image on the input side.
光从左向右传播、透镜位于 x 等于零处、实物位于 x 为负处时，实像位于 x 等于 s 撇的正值处；s 撇为负则虚像位于入射一侧。
State the convention before substitution, as other signed-coordinate conventions give different-looking equations.
代入数值前先说明所用约定，因为其他带符号坐标约定会给出形式不同的方程。
For a converging thin lens, a ray parallel to the axis exits through the far focal point, and a ray through the ideal optical centre continues undeviated.
对于会聚薄透镜，平行于主轴的光线穿过远焦点射出，通过理想光心的光线方向不变。
Their intersection identifies a real image; backwards extensions can locate a virtual image.
它们的交点确定实像；反向延长线可定位虚像。
The paraxial approximation uses rays close to the axis and neglects thickness and aberrations.
近轴近似使用靠近主轴的光线，忽略厚度和像差。
With s greater than f, and f positive, s prime is positive and M is negative; the image is real and inverted.
当 s 大于 f 大于零时，s prime 为正且 M 为负：成倒立实像。
With s between zero and f, s prime is negative and M is positive; the image is virtual, upright and enlarged.
当零小于 s 小于 f 时，s prime 为负且 M 为正：成正立放大虚像。
At s equal to f, the emerging rays are parallel and no finite image plane exists.
当 s 等于 f 时，出射光线平行，不存在有限像面。
A diverging lens with a real object produces an upright, reduced virtual image.
发散透镜对实物成正立缩小虚像。
For a spherical mirror in the same real-is-positive convention, a concave mirror has positive f and a convex one negative f, with f equal to R over 2 in the paraxial limit.
对于采用相同实为正约定的球面镜，凹面镜的焦距f大于零，凸面镜的焦距f小于零，在傍轴近似下f等于R除以2。
A real reflected image is in front of the mirror on the incoming-light side; a virtual image is behind it.
实反射像位于镜面之前、入射光一侧；虚像则位于镜面之后。
Thus a positive image distance has a different physical side for a mirror than for a transmitting lens.
因此，正像距对镜面而言与对透射透镜而言具有不同的物理侧。
A parallel ray reflects through the concave focus; a ray aimed through the centre of curvature retraces its path.
平行光线经凹面镜反射后通过焦点；指向曲率中心的光线将沿原路返回。
Convex reflected rays diverge as if from the focus behind the mirror.
凸面镜的反射光线发散，仿佛来自镜后的焦点。
Use the same equation and magnification M equal to minus s prime over s with signed values, rather than silently combining mirror geometry with a lens coordinate diagram.
请使用同一公式及M等于负s撇除以s（带符号值），而非静默地将镜面几何与透镜坐标图合并处理。
For a sequence of separated lenses, first calculate the actual image coordinate from the first lens.
对于分离透镜序列，首先计算第一透镜的实际像坐标。
Relative to the next lens, decide whether the incoming rays diverge from a point before it or are still converging toward a point beyond it; these are real and virtual objects respectively.
相对于下一个透镜，判断入射光线是从其前方某点发散，还是仍在向其后方某点会聚；前者为实物，后者为虚物。
Only then assign its signed object distance and solve again.
然后为其分配带符号的物距并重新求解。
Total transverse magnification is the product of the individual signed magnifications for aligned paraxial elements.
总横向放大率是各对齐近轴元件带符号放大率的乘积。
Element separation is not automatically the second object distance.
元件间距并不自动等于第二物距。
Geometric real/virtual character depends on convergence, not on whether the final image is magnified.
几何上的实或虚性质取决于光线的会聚情况，而非最终像是否被放大。
These ideal results do not model wave-optical resolution or spherical/chromatic aberration.
这些理想结果不模拟波光学分辨率或球差、色差。
Take a converging lens with f equal to 12 centimetres and a real object at 8 centimetres.
取焦距 f 为 12 厘米的会聚透镜，实物位于 8 厘米处。
One over s prime is one twelfth minus one eighth: minus one over 24 centimetres.
s′ 的倒数等于十二分之一减八分之一：负二十四分之一每厘米。
So s prime is minus 24 centimetres, and M is minus s prime over s: plus 3.
所以 s′ 等于负 24 厘米，M 等于负 s′ 除以 s：正 3。
The image is virtual, upright and three times larger, on the object's side of the lens.
像是虚像、正立、放大三倍，位于透镜的物体一侧。
The negative distance tells you the side; it is not an arithmetic failure.
负的距离告诉你像在哪一侧；它不是计算错误。
A converging lens at x equals 0 has f sub 1 equals 10 centimetres and a real object at x equals minus 30 centimetres.
位于 x = 0 处的会聚透镜焦距 f₁ = 10 cm，实物位于 x = -30 cm。
A second converging lens of f sub 2 equals 10 centimetres is at x equals 10 centimetres.
第二块焦距 f₂ = 10 cm 的会聚透镜位于 x = 10 cm 处。
Locate the final image and calculate total signed magnification.
请定位最终像并计算总符号放大率。
Identify the second lens's object as real or virtual.
判断第二透镜的物是实物还是虚物。
First image has s sub one prime equals 15 centimetres and M sub one equals negative one half.
第一像的 s₁' = 15 cm，M₁ = -1/2。
The second lens intercepts converging rays headed to x equals 15 centimetres, so s sub two equals negative 5 centimetres: a virtual object.
第二透镜拦截了会聚向 x = 15 cm 的光线，因此 s₂ = -5 cm：这是一个虚物。
One over s sub two prime equals one over 10 minus one over negative 5, which equals three tenths per centimetre, hence s sub two prime equals 10 over 3 centimetres.
1/s₂' = 1/10 - 1/(-5) = 3/10 cm⁻¹，故 s₂' = 10/3 cm。
Final coordinate x equals 10 plus 10 over 3, which is 40 over 3 centimetres; M sub two equals negative s sub two prime divided by s sub two, which is 2 over 3; total M equals negative one third.
最终坐标 x = 10 + 10/3 = 40/3 cm；M₂ = -s₂'/s₂ = 2/3；总放大率 M = -1/3。
Award first image, signed second object, second image, final coordinate and magnification.
评分要点包括：第一像、带符号的第二物、第二像、最终坐标及放大率。
The final image is real and inverted.
最终像是实像且倒立。
Keep signs until the geometry is interpreted; a positive mirror image lies on the incident side, while a positive transmitting-lens image lies on the outgoing side.
在几何关系明确之前，请保留符号。 正号镜面像位于入射侧，而正号透射透镜像位于出射侧。
virtual image: An apparent image located by backwards ray extensions rather than actual outgoing-ray convergence.
虚像：通过反向光线延长线确定的表观像，而非实际出射光线的会聚点。
transverse magnification: Signed image-height to object-height ratio, −s′/s in the declared convention.
横向放大率：带符号的像高与物高之比，即负s撇除以s，遵循所声明的符号约定。
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。