Justin Peatross 和 Michael Ware 兩位先生解釋『成像條件』

 

宛如順手捻來不費力氣！甚至三言兩語說明了經典的『幾何光學』三條線！！

 

此處僅補之以『幾何』的推導︰

 

上圖且將『物』 、『像』 多畫幾次。同時參照 Figure 9.14 ，依相似三角形可得︰

，

，兩式相加後即是『成像公式』

的了。作點簡單代數運算，即可將此式改寫為

。這就是牛頓成像公式的哩。

若問這麼清楚明白的事能有懸念乎？假設位於透鏡前焦距之前之物 ，形成倒立實像，人可以見得著嗎？？相機能夠拍得到耶？？！！何不秉持實證精神，自己檢驗一番呢！！？？

Image formation with a lens

Procedure

---

a Lenses forming real images

Face away from the window, holding a sheet of paper at arm’s length. Hold the lens in front of the paper and move it to and from the paper (towards you and back towards the paper) until you see an image of the window on the paper.

b Real image with and without screen 

Hold a lens at arm’s length towards the window. Hold a piece of greaseproof paper in the other hand and find the place between the lens and your head where there is a clear image of the window on the paper. You are looking at that image through the paper. Your eyes should be focused on the paper itself.

Remove the paper and look at the image in space. If you cannot find the image put the paper back and repeat the process. It may be helpful to catch half the image on the edge of the paper and the other half in space. Concentrate on the image on the paper and slide the paper away.
………

 

請讀者然後細思

 

，到底宣說何理呦？？？

【※ 隨文附註】

pi@raspberrypi:~ $ ipython3
Python 3.4.2 (default, Oct 19 2014, 13:31:11) 
Type "copyright", "credits" or "license" for more information.

IPython 2.3.0 -- An enhanced Interactive Python.
?         -> Introduction and overview of IPython's features.
%quickref -> Quick reference.
help      -> Python's own help system.
object?   -> Details about 'object', use 'object??' for extra details.

In [1]: from sympy import *

In [2]: from sympy.physics.optics import FreeSpace, FlatRefraction, ThinLens, GeometricRay, CurvedRefraction, RayTransferMatrix

In [3]: init_printing()

In [4]: do1, di1, f1, do2, di2, f2 = symbols('do1, di1, f1, do2, di2, f2')

In [5]: RealImage = RayTransferMatrix(-di1 / do1, 0, - 1 / f1, -do1 / di1)

In [6]: RealImage
Out[6]: 
⎡-di₁        ⎤
⎢─────    0  ⎥
⎢ do₁        ⎥
⎢            ⎥
⎢ -1    -do₁ ⎥
⎢ ───   ─────⎥
⎣  f₁    di₁ ⎦

In [7]: ViewImage = FreeSpace(di2) * ThinLens(f2) * FreeSpace(do2) * RealImage

In [8]: ViewImage
Out[8]: 
⎡      ⎛  di₂    ⎞             ⎛  di₂    ⎞       ⎛          ⎛  di₂    ⎞⎞ ⎤
⎢  di₁⋅⎜- ─── + 1⎟   di₂ + do₂⋅⎜- ─── + 1⎟  -do₁⋅⎜di₂ + do₂⋅⎜- ─── + 1⎟⎟ ⎥
⎢      ⎝   f₂    ⎠             ⎝   f₂    ⎠       ⎝          ⎝   f₂    ⎠⎠ ⎥
⎢- ─────────────── - ─────────────────────  ─────────────────────────────⎥
⎢        do₁                   f₁                        di₁             ⎥
⎢                                                                        ⎥
⎢                      do₂                             ⎛  do₂    ⎞       ⎥
⎢                    - ─── + 1                    -do₁⋅⎜- ─── + 1⎟       ⎥
⎢            di₁        f₂                             ⎝   f₂    ⎠       ⎥
⎢           ────── - ─────────                    ─────────────────      ⎥
⎣           do₁⋅f₂       f₁                              di₁             ⎦

In [9]: ViewImage.B
Out[9]: 
     ⎛          ⎛  di₂    ⎞⎞ 
-do₁⋅⎜di₂ + do₂⋅⎜- ─── + 1⎟⎟ 
     ⎝          ⎝   f₂    ⎠⎠ 
─────────────────────────────
             di₁             

In [10]: