物理

這份報告的主題是藉由實驗，來探討雷射光的性質及它的應用，並實際製作利用雷射光原理的小器具。1.證明雷射光是否為單色光：先將雷射光射入不同顏色的玻璃紙，利用光無法穿透不同顏色玻璃紙的性質，以及將雷射光照射三稜鏡，觀察其反射的光線，藉此來證明雷射光是否為單色光。2.雷射光的直進性質：利用彎管或其他不透光物品將光線阻擋，觀察其是否能穿透物品，並且用不透光物質，使我們能夠看出雷射光的軌跡，來證明雷射光的直進性質。3.雷射光的折射與反射：將雷射光射入不同的物質中，觀察其折射角度，來得知雷射光在不同介質中的傳播速率不同，也觀察其是否有反射的現象。4.雷射光的應用：研究運用雷射光製成的物品，如雷射印表機、光碟機等等，並了解其製作原理。5.自行研製雷射小器具：利用雷射光的原理，來製作簡單而獨特、有效率的小器具。The topic of this report is to study the quality and applications of laser by experiments, and actually make a tool by using the principles of laser.1.Prove if laser is a one-color light: By lasing laser through a triangular prism, observe the light it reflected to prove that laser is a one-color light.2.The quality of in-line approach: By using tubes or other lightproof items to block out the light to observe if it can penetrate things, and also let us see the trace of laser to proof the quality of in-line approach.3.The refraction and reflection of laser: Study the differences of refracting angles by lasing laser into different items, to know the speed of laser in different mediums, and also observe if it will have any reflections.4.The applications of laser: Understand how laser products are made by studying them, like laser printers and CD players. 5.DIY laser tools: Make simple but unique and efficient tools by using the principles of laser.

溶液和溶劑置於同一容器中，當溶質向上擴散時，會形成濃度梯度及\r 折射率梯度dn/dy，且dn/dy 對高度y 的關係圖會呈現隨著高度改變的現\r 象。\r 半徑r 的Ｄ形容器，下方置溶液，上方置溶劑，以雷射光照射容器的\r 平面部份時，雷射光沿著法線出射，受折射率梯度的作用而向下偏Ζ距\r 離，a 為容器至屏的距離，得到dn/dy=Z/ar 的關係式；改變雷射光的高\r 度y 可得dn/dy 圖。\r 以硫代硫酸那作實驗，其dn/dy-y 圖為以原始界面為對稱軸，因其擴\r 散係數不隨濃度改變；甘游水溶液的dn/dy-y 圖呈現不對稱，圖形的極\r 大值往甘油方偏，主要係因為甘油的擴散係數隨濃度的增大而減少。\r 我們成功第把不同時間對同一溶液的實驗結果予以模型化，得到的\r dn/dy-y 曲線隨時間改變，並發現該曲線所涵蓋的面積為定值。\r \r The mixing in a vertical column between a pure liquid and a solution produced a concentration gradient, which in turn produced the refractive index gradient. As the solute particles diffused upward into the pure liquid, the gradient was generated by the varying solute concentration. The plot of the refractive index gradient versus vertical position y (dn/dy vs y) is found to be varied with time. A D-shape container of radius r is partly filled with denser solution, and partly filled with solvent which is on the top of solution. When laser beam enters perpendicularly to the flat surface of the container, the outgoing beam strikes the container at normal incidence, and deflected down a vertical distance Z by the refractive index gradient. We can get dn/dy=Z/ar, where a is the distance between the container and the screen,. By changing the vertical position (y) of laser beam, we can get the plot of dn/dy vs y. For a sodium thiosulfate-water solution, the trace of dn/dy vs y is symmetric with respect to the position of original boundary. Since the diffusion coefficient of sodium thiosulfate is independent of concentration. For the trace of dn/dy vs y of a glycerol-water solution, it will no longer be symmetric. A skewed curve which reaches its maximum position is displaced to the glycerol side, because the diffusion coefficient of glycerol is decreased with concentration. We have successfully modeled the time-dependent experimental gradient curves on the same solution. The trace of dn/dy vs. y at different time is found to keep the area constant.

Nd-YAG Laser 是目前最常被用來當作Pumping Source(汲發光源)，較早期是使用discharge lamppumping，但是閃光燈的發光頻率並非完全落在Nd-YAG 晶體的吸收帶上，因此大量的能量轉變為熱能，十分的浪費能源，且增加冷卻系統的負荷。因為discharge lamp pumping 是一種氣體放電的過程，每次放電的時間和能量都有很大的不穩定性。所以高效率、高穩定性的Laserdiode 便成為pumping source 的另一種選擇。在此實用價值下，便決心以一組Laserdiode Pumped Nd-YAG Laser的套件，使用AlGaAs Laserdiode 作為pumping source，來汲發Nd-YAG 晶體，所有物件被固定在同一個rail(軌道)上，從對光到汲發晶體(增益介質Nd-YAG 晶體)，到產生1,064nm 的紅外光雷射，及其倍頻532nm 的綠光雷射，正可作為一完整的雷射訓練過程。

某次於學校的科學表演中，見到黑白陀螺在旋轉後會產生顏色的\r 變化，使人印象深刻。文獻上記載此類陀螺稱為“Prevost”圓盤，\r 其色彩產生的原因一般被認為是人眼產生之錯覺。不過究竟為何會有\r 這種錯覺，總令人相當納悶。於是我們請教了老師，不僅做了實驗，\r 也用像機拍攝下來分析，不過令我們感到奇怪的是：如果是眼睛產生\r 的錯覺，又為何能拍出顏色？甚至，在研究的過程中我們意外的觀察到鏤空圓盤內的色塊裡，\r 尚有像水波「波紋」般的條紋出現。這個現象十分奇特，於是我們設\r 計了一系列的實驗去探討這些現象，開始了這次的研究。在研究過程中我們遇到相當大的困難，所幸同伴的程式設計技術\r 卓越。為了實驗也撰寫了許多套色彩分析程式，使得實驗更能得心應\r 手。而我是負責實驗儀器的架設及實驗操作，希望能以分工合作的方\r 式，來完成這次的研究。

本實驗一開始主要探討超聲波在水中的基本性質，如：指向性、衰減性…等。實驗發現，超聲波的衰減會同時與其指向性以及衰減性有關。 接著希望利用超聲波在水中的物理性質，近一步測量超聲波在水中的聲速，實驗中則利用駐波以及聲光效應測量。在駐波法測量聲速的實驗中，用洗淨機當作聲源，內部放置量筒，量筒內盛水後放入木屑，並使聲波在其中產生駐波即聲浮現象，求出波長後反推聲速，測量出的聲速誤差值僅有1.13%，而在使用聲光效應測量聲速的實驗中，使1.65 MHz 的超聲波在自製的壓克力容器內部所裝的水中產生駐波後，以波長650 nm 的紅光雷射通過，在遠處屏幕即產生似於光柵繞射現象，藉著屏幕上的繞射條紋反推該液體聲速，測量出聲速誤差均在5%以下。 在觀察聲光效應實驗中，發現過段時間後有氣泡產生，由文獻上，得知此現象為超聲空蝕現象(Acoustic cavitation)，就設計實驗測量聲場中聲壓分部，並利用蠟紙觀察氣泡的成長。實驗發現聲場中的聲壓強度以及液體的表面張力和蒸汽壓會影響到產生空蝕的臨界值及產生氣泡的數量。 ;At the beginning this experiment explores the ultrasonic base in the water, including its velocity, the physics property of liquid, direction, and attenuation etc. . . At first, we use methods of standing wave to measure the velocity of sound under the water, using an ultrasonic cleaner as the sound source and putting some wooden powder in the water. As the standing wave accrues/produces, the powder will “stand still.” To measure the length between two grains of powder, in this way we can calculate sound velocity. Another method we use is diffraction of optics. Put 1.65 MHz source and water in a transparent container; then using laser through it. At the board much diffraction light stripes are created. By this way, we can estimate the velocity. Following these ways can calculate velocity precisely. In these experiments, some bubbles create in the container are discovered. We learn it is so-called “Acoustic Cavitation” based on the reference paper. Besides, we design experiment to know the bubbles’ growth and the number of the bubbles is connected to the physics property of liquid. We use different kinds of liquid with different vapor pressure and surface tension. Finally, we know when it has the smaller surface tension and bigger vapor pressure, the liquid makes bubble velocity grow faster and larger amount of bubbles are produced.

在本次實驗中，我發現膠狀電解質溶液中的帶電離子，會因為離子團的熱運動，和電偶極的庫倫吸引力 (electric dipole) 的交互作用下，使溶液的I-V curve (電流-電壓曲線)，具有類似磁滯曲線(Hysteresis curve) 的效果；而膠狀溶液之濃度越高，電解起始點的對應I-V 值也越大。此外，白金電極與銅箔電極的距離若改變，也會使溶液的I-V curve 變的不一樣。另一方面，我也發現，在給予膠狀電解質溶液一緩慢外加的電壓或衝擊電壓並持續維持此一定額外加電壓時，會因為該溶液的黏度持續增高、帶電離子濃度增高且反應不斷變化下，而使該溶液的對應電壓，形成一重複出現「先降-後升-再降」的震盪現象，且電壓值節節升高。最後，我利用掃描式電子顯微鏡（SEM）及能量分散光譜儀（EDS）觀察銅箔電極之表面變化並分析其上之化學組成，藉此嘗試解釋上述這些有趣的現象。In this experiment, with the interaction of the heating action of ionic atmosphere and electric dipole, I find that ions in the gel make the I-V curve in the colloid electrolyte liquor show up with the effect similar to Hysteresis curve. The higher concentration of the colloidal solution, the bigger value of I-V at the initial electrolysis reaction was found. Furthermore, the shape of I-V curve is dependent on the distance between platinum electrode and cupper electrode. On the other hand, I find that when I apply a gradual extra-voltage or a fast extra-voltage to the colloidal electrolyte solutions and then maintain to a fixed value, this will make a unique ‘two peaks’ state oscillation of corresponding voltage. The reason is owing to the climbing viscosity and ion concentration in the solution. With the methods of scanning electron microscope (SEM) and energy dispersive spectrometer (EDS), I observe the change and analyze the components of chemicals on the surface of the cupper electrodes. Finally, I present the interesting results and try to interpret these phenomena.

Up to this time we have spent almost three years in studying condensation and water droplets. Little could we have done as compared with the almighty nature. However we are rewarded by the nature as we gradually found the secrets about electro-magneto field and water droplets: The size of water droplets turn smaller upon electro-magneto field and grow more uniformly especially upon electric field. This experiment presented here is actually the diary of the growth of water droplets in condensation, upon magnetic field and electric field. Through convection, it discusses the self assembly patterns of water droplets and peep into the uniformity both of the size and the distribution mode of water droplets. In former basic experiment, we focus on temperature and the speed of water moisture; generally speaking, higher temperature speeds up the coalescence procedure but does not affects the nucleation size of water droplets in simple plain surroundings; while speed of moisture does affects the nucleation size. As we went farther, deep into convection and found magneto-electric force did play an important role in the self assembly mechanism of water droplets. The topic is mostly concerned as we are surrounded by magneto-electric waves in today’s world. This experiment anchors the first step in discovering the uniformity of water droplets in different environment, and providing insights into the self assembly mechanism of water droplets upon electro-magneto field with nano sizes. 這是一系列關於水蒸氣冷凝為極細微小水珠的實驗。其中可以分為兩大部分； 第一部分是基礎實驗。將水蒸氣導入至潔淨的介面上(蓋玻片)，觀察冷凝水珠的結構。雖然看似簡單平常，但卻有令人驚奇的發現；不同溫度的水蒸氣，其冷凝最初始的細微顆粒之尺寸是相同的 ！爾後隨著溫度的升高，堆疊速率也跟著上升；以致於最後一起呈現出來的水珠大小不一，尺寸不一。 第二部分是將水蒸氣導到磁場及靜電場上，觀察其冷凝結構。這部分的實驗推翻了一般「水分子是電中性在電磁場中不受影響？」的刻板觀念 ！實驗所呈現出來的冷凝水珠，不但於附加磁場中尺寸縮小又不易長大，同時還有固定的自我組成模式( Slef-assembly pattern);而且也發現在磁場中的冷凝小水珠的尺寸比電場中的小，可是電場中的小水珠則表現出較大的均勻特質。

本實作以光學全像術為基礎，拍攝出三維立體的影像。內容主要為分別製作「穿透式」全像片、「反射式」全像片及「彩虹」全像片等三部份。其中，在反射式全像片中，嘗試以不同數量的光束來拍攝。發現以單光束法拍攝出的全像片比較容易成功，但重建影像的視角與效果都不如雙光束拍攝法來的好。在拍攝彩虹全像片的過程中我們令狹縫為變因，做有加狹縫與未加狹縫的實驗，實驗發現效果不同。並以改變狹縫的角度、方位，來觀察底片的變化。最後，觀察出豐富多樣的彩虹變化型態。全像片可重建拍攝的物光與參考光，並顯現拍攝物的三維狀態。可應用於信用卡、紙鈔防偽，廠商標籤，附加商品（如鑰匙圈、貼紙），廣告看板等，用途廣泛。 The purpose of this project is to construct the 3-dimensional images utilized optical holography. The holograms we made can be categorized into three main types: transmission, reflection and rainbow. In reflection hologram, we have tried to construct the hologram by the use of different number of light beams. It could be found that the reconstructed image of the hologram formed by a single beam is better than those of the hologram formed by two beams. However, the field of view and image quality of the two-beam hologram was better than those of single-beam hologram. In rainbow hologram, we varied the orientation and position of slit to investigate the quality of the reconstructed images. The reconstructed images displayed rainbow image diversity. In application, the holograms can display three-dimensional images by reconstructing the hologram. In addition, the holograms are in widespread applied in security applications of credit card、banknotes、labels、stickers etc.

當流體由圓管流下，在碰撞到物體後水流會產生類似駐波的形狀。為瞭解此現象的產生機制，及影響此現象的變因，我們改變流體的表面張力、流速及與碰撞物體間的距離，以探討各變因對波形所產生的影響，進而研究此現象的成因。由實驗結果發現波形會因流速加快、擋板距離增加、表面張力減少而有波長變短的趨勢，且可以用表面張力波的理論解釋。由理論推導的結果，可測量液體表面張力。由於圓球狀的外型使表面積增大，可增加液體之散熱的面積，因此可應用在水冷系統方面。A phenomenon similar to the standing wave, which occurs when a slow-velocity fluid jet collides with an obstacle, was observed. Because the free surface profile was observed to be stable, the phenomenon was not considered as standing wave. To understand the mechanism of this phenomenon and the factors that can affect the free surface profile, the surface tension of the fluid, jet velocity and the distance between the exit of the tube and the obstacle are varied to study their influences on the free surface profile. According to our experiment, the wave length is shortened when the jet velocity or the distance between the tube and the obstacle increases or when the surface tension decreases. The tendency of the investigated phenomenon can be explained by the capillary wave theory. Based on Bernoulli’s principle, continuity principle and surface tension\r equation, an ODE (ordinary differential equation) could be formulated. By using numerical method to solve this ODE, we predict the free surface profile which could match the experimental photo well. The tendency of the phenomenon can also be explained by the ODE. In order to measure the surface tension of the fluid, we wish to minimize the experiment apparatus. To enhance our assumption we use laser to locate the individual particle that we add in the fluid and calculate the velocity field of the flow jet.

在高中光學裡，介紹了許多有關光波之特性，而聲波與光波皆具有波動性，因此聲波應具有如干涉、反射、聚焦等特性，但在物理課本上並未詳加敘述，所以我們開始了本項的研究，希望可以籍由改變聲源及邊界的各項條件，而探討其發生之現象。在本研究中，我們利用聲波之基本原理在電腦上進行聲場的模擬並加以改變其變因（頻率、相位、聲源數、聲源間距、強度、邊界反射），進而明瞭聲場之各項特性及應用與控制方式。經電腦模擬聲場圖中，我們觀察到，兩聲源干涉所形成之圖形為多組雙曲線所組成，近似於光學之雙狹縫干涉，增加聲音頻率與聲源間距離皆可使腹(節)線數目增加。如同現實世界中所知的，隨著頻率的增加，將會具有指向性的產生並且在聲源數目越多時越明顯，但發現頻率增加至一定值之後，指向性反而會降低而形成冠狀面。在延遲了多點聲源間相位之後，聲場分佈有偏轉之現象，利用相位延遲的方法，在多聲源中，將兩旁之聲音偏向中央將可造成聲音的聚焦。在兩聲源干涉中，調整其中一聲源之強度，將可完全消除兩音源連線間一點之聲音，可適當的應用在工業上消除噪音。聲場分佈在具有邊界的環境下，我們試著找出聲源位置及邊界條件對聲場分佈的影響與關係以模擬室內聲場，但在簡化的數學模式下，即無法有我們所希望之最均勻聲場分佈產生。最後我們將實驗中的結果與文獻上的實驗數據加以比較，以探討其誤差。 The optical course in senior high school , which introduced many characteristics of optical wave. However, both of sound and light have the characters of wave; therefore, sound wave should have the characteristics, such as interference, reflection and focalizing. Nevertheless, there are not many details of sound wave in the section of acoustic on our textbook. So we began this research, and discuss the different phenomena by changing many kinds of variables. In our research, we simulated the sound field on the computer, based on sound wave’s principle, furthermore we change many variables, which like frequency, phase, source number, distance, intensity and reflection. It helps us understand the characteristics of\r sound, how to control sound and how to apply these findings. According to the result of computer simulation, we discovered that the graph of two acoustic source’s interference comprised by many pairs of hyperbola, just like optical double slit interference. As the frequency or the sound source distance increased, acoustic direction became more and more obvious. But when the frequency was high enough to over the extreme, instead increasing, the acoustic direction would lower down like a crown. After we make phase differences on one of the two sound sources, sound field generated\r deviation. So if we use this method in multiple sound source, and delay the middle source, the sound field might be converged. In such two-sound-source interference pattern, when we control the intensity of one, a certainly point on the line of the two sources disappeared When the sound field enclose by borderline, the standing wave appear, and we discovered many funny phenomena. We put large amount of source in a narrow slit, the phenomenon of diffraction appeared. Finally, we discussed the discrepancies between interference pattern previously done by others experiments and the simulated one conducted by us.