Part V. Optics 第五部: 光學 Reflection & Refraction 反射和折射 Images & Optical Instruments 影像和光學器材 Interference & Diffraction 干涉和繞(衍)射

Drops of dew act as miniature optical systems, 露水珠形成微形光學系统， with light refracting through the drops to form myriad images of the background flowers 光經過水珠折射後，把在背景的花朶形成眾多的影像 －which themselves are out of focus in the photographer’s camera. －花朶本身則在攝影師鏡頭的焦點之外。

30. Reflection & Refraction 反射和折射 Total Internal Reflection 全反射 Dispersion 色散

Why does the bee’s image appear at left, 為甚麼蜜蜂的影像會出現在左邊， and what does this have to do with e-mail and the Internet? 這跟電子郵件和國際網路有何關係？ Ans: Total internal reflection; fibre optics. 答： 全反射; 光纖。

30.1. Reflection 反射 Conductor: E of light drives e to oscillate 導體：光的 E 驅使 e 擺動  re-radiate  再輻射  reflection  反射 Huygens-Fresnel principle 惠更斯-菲涅爾原理: Each point of an advancing wave front is the source of new (spherical) waves. 在前進中的波面上，每一點都是新的(球面)波的源頭。 The new wave front is tangent to all these waves. 新的波面與這些波全部相切。 angle of incidence = angle of reflection 入射角 = 反射角  = 

Specular reflection 鏡面反射 ( smooth surface 平滑表面 ) Diffuse reflection 彌漫反射 ( rough surface 粗糙表面)

Example 30.1. The Corner Reflector 角落反射器 Two mirrors join at right angles. 兩面鏡子成直角。 Show that any light ray incident in the plane of the page will return anti-parallel to its incident direction. 請証明任何在紙面上的入射光線，反射後都與入射方向反平行。 Ray turned by angle B here 光射在此的轉角為 B Ray turned by angle A here 光射在此的轉角為 A

Partial Reflection 部份反射 ， Continuity of fields at boundary 場在邊際處連續  incident waves always partly reflected. 入射波一定有部份被反射 Least reflection at normal incidence (4% for glass). 垂直入射時反射最小 (玻璃為4%) Anti-reflection coating for lens, solar cells… 反反射膜可加於鏡片，太陽能胞…

30.2. Refraction 折射 Wave speeds differ in different media. 波在不同介質中的速度不等 index of refraction 折射率 Observers at A & B count same number of wave crests at any given duration 在 A 和 B 處的觀察者在任何時段中數到的波峯數目都一樣 wave frequency doesn’t change in crossing media. 波的頻率在跨越介質後保持不變。  smaller for medium with slower v or higher .  在 v 較慢或 n 較大的介質中較小。

Table 30.1. Indices of Refraction

1 1 2  Snell’s law

Example 30.2. Plane Slab 平面板 A light ray propagating in air strikes a glass slab of thickness d and refractive index n at incidence angle 1. 一條在空氣中的光線以角度 1 入射一塊厚度為 d ，折射率為 n 的玻璃平板。 Show that it emerges from the stab propagating parallel to the original direction. 請証明它離開玻璃板時的方向與原來的平行。 At 1st (upper) interface 在第一個(上方)介面 At 2nd (lower) interface 在第二個(下方)介面 Since 因

Example 30.3. CD Music 光碟音樂 The laser beam that reads information from a compact disc is 0.737 mm wide when it strikes the disc, and it forms a cone with half angle 1 = 27.0. 閱讀光碟資訊的圓錐形雷射光束在碰到光碟時，寬 為 0.737 mm，半角為 1 = 27.0。 It then passes through a 1.20 mm thick layer of plastic with refractive index 1.55 before reaching the reflective information layer near the disc’s top surface. 之後它要通過一層 1.20 mm厚，折射率為 1.55 的塑料，才能達到位於光碟上方的反射性資訊層。 What is the beam diameter d at the information layer? 光束在資訊層的直徑 d 為何？ At the incidence (lower) interface 在入射 (下方) 介面處 : At the information (upper) surface 在資訊層 (上方) 表面 :

GOT IT 懂嗎 ? 30.1. The figure shows the path of a light ray through three different media. 圖中光線穿越三層不同的介質。 Rank the media according to their refractive indices. 請以折射率為這些介質排序。 n3 > n1 > n2

Multiple & Continuous Refraction 多次和連續折射 Increasing n. n 增大 Actual light path 真正的光線 Apparent light path 感到的光線 Mirage appears here 幻像在此 Air’s temperature-dependent refractive index results in the shimmering mirages you see on highways. 空氣的折射率與温度有關，因此做成你在高速公路上看到的閃爍幻像。 What you’re actually seeing is refracted sky light. 你看到的其實是經過折射的天光。

Refraction, Reflection, & Polarization 折射，反射和極化 Incident beam with in-plane polarization 入射光束的偏極在入射面上: no reflection when 當 refr = p  Brewster (or polarizing) angle 布儒斯特(偏振)角 時即無反射 ( reflected beam longitudinal: not EM ) 反射光束為縱波：不是電磁波 p  56 for air-glass 空氣-玻璃 Reflected light is perpendicularly polarized if incidence is at p . 光以 p 入射時，反射光垂直偏極。

30.3. Total Internal Reflection 全反射 Critical angle c for total internal reflection ( refr  90 ) 全反射 ( refr  90 ) 的臨界角度 c n1 > n2

Example 30.4. Whale Watch 賞鯨 Planeloads of whale watchers fly over the ocean. 載滿賞鯨客的飛機在海洋上空飛翔。 Within what range of viewing angles can the whale see the planes? 在甚麼角度之內鯨魚才能看見這些飛機？ The whale sees the entire world above the surface in a cone of half-angle θc ; 鯨魚看到整個在水面以上的世界都在一個半角為 θc 的圓錐體內； beyond that, it sees reflections of objects below the surface. 在此以外，它看到水面下物體的反射。

GOT IT 懂嗎 ? 30.2. The glass prism in figure has n = 1.5 and is surrounded by air ( n = 1 ). 圖中的玻璃棱鏡 n = 1.5 ，其外四周是空氣 ( n = 1 ) 。 What would happen to the incident light ray if the prism is imersed in water ( n = 1.333 )? 如果把棱鏡沈在水 ( n = 1.333 ) 中，光入射後會怎樣？ Most of it emerges into the water at the diagonal interface; with only a small part still reflected. 大部份在斜面處進入水中；小部份依舊反射

Application: Optical Fibre 應用：光纖 Typical fibre: glass core of d = 8 m, cladded by smaller n glass. 典型的光纖：核心玻璃 d = 8 m ，外包以 n 較小的玻璃。 total internal reflection 全反射 Typical transmission ~ km. 典型的傳送 ~ 公里。 SemiC laser 半導體雷射 :  = 850, 1350, 1550 nm Required bandwidths 需用頻寬 : Audio 語音 : kHz TV 電視 : 6 Mhz Microwave freq 微波的頻率 : 1010 Hz Light freq 光的頻率 : 1014 Hz

30.4. Dispersion 色散 v depends on   n depends on  : dispersion v 與  有關  n 與  有關 : 色散 Dispersion separates the colors in white light, with shorter- wavelength violet experiencing the greatest refraction. 色散把白光中的顏色分開，較短波長的紫光的折射較強。

Rainbow 彩虹 Double rainbow and supernumerary rainbows on the inside of the primary arc. 雙層彩虹和在主弦內的多餘彩虹。 The shadow of the photographer's head marks the centre of the rainbow circle (antisolar point). 攝影師的頭的影子就是彩虹圓圈的中點 (背日(光)點)。

The primary rainbow results from total reflection in raindrops that concentrates light at approximately 42° deflection. 主彩虹源於雨滴內的全反射把光集中於42°反射角。 Dispersion separates wavelengths slightly, resulting in the rainbow’s colors. 色散把波長稍為分開，做成彩虹的色彩。 The rainbow is a circular arc located at 42 ° from the line that connects the Sun, the observer, and the center of the arc. 彩虹是一個圓形的弧，與連接太陽，觀察者，和弧心的直線的張角為 42 ° 。

Light rays enter a raindrop from one direction (typically a straight line from the Sun), reflect off the back of the raindrop, and fan out as they leave the raindrop. 光線從一方進入雨點 (通常是從太陽來的直線) ，在雨點後方反射，離開雨點時散開。 The light leaving the rainbow is spread over a wide angle, with a maximum intensity at 40.89–42°. 光離開彩虹時會散開很大的角度，強度最高的約在 40.89–42° 間。 White light separates into different colours on entering the raindrop because red light is refracted by a lesser angle than blue light. 白光進入雨點後分成各種顏色，因為紅光比藍光折射得少。 On leaving the raindrop, the red rays have turned through a smaller angle than the blue rays, producing a rainbow. 離開雨點時，紅光轉的角度比藍光小，於是做成彩虹。

Glass lenses: chromatic aberration. 玻璃鏡片：色差 The spectrum of a diffuse gas－here hydrogen－consists of light at discrete wavelengths. 稀簿氣體－此處為氫氣－的光譜由波長不連續的光組成。 Glass lenses: chromatic aberration. 玻璃鏡片：色差 Varying ionization level in ionosphere 電離層中電離程度的差異  dispersion in radio waves  無線電波的色散 Comparing travel times of radio waves of different freq reveals atmospheric conditions 比較不同頻率的無線電波的傳送時間可以顯示大氣的狀況  dual-freq GPS with cm resolution  雙頻式全球定位系統，解析度可達公分。