國王的海市蜃樓
在夏日的午後，在炎熱的柏油路面上很容易可觀察到遠方的 路面上，出現如鏡子般的倒影，看起來彷彿前方有一灘水，但當 我們向前進一些時，倒影卻突然消失了，這個現象，一般稱為海 市蜃樓。 一般解釋海市蜃樓的成因，都是由於在上層的低溫空氣，和 在下層靠近路面的高溫空氣，因密度的不同，以致於折射率的漸 層差異，繼而產生全反射。 但我們觀察發現，地面與上層空氣的溫差，並非柏油路面上 假積水現象及倒影出現的必要條件；反而和入射光的角度、路面 的平坦程度及路面的性質有關。我們提出了粗糙面在入射光的入 射角接近90度時，可發生單向反射的模型。並由實驗來驗證假積 水現象及倒影主要的成因是「柏油路面的單向反射」而非「空氣 的折射與全反射」。 Under the scorching sunshine, we can see the reflection on the tarmac in the distance just like a water puddle on the road. And the water also reflects the people and object nearby. But, in fact, the tarmac road over there is very hot and dry. Therefore we call the phenomenon as the “false water puddle on the tarmac.” According to the textbook , the main reason for “false water puddle on the tarmac” is that the temperature difference leads to the refraction of the light and causes the phenomenon. However, from our observation, the theory still can’t explain some phenomenon, For example, the “false water puddle on the tarmac” remains to appear when the wind blows fiercely. Even with little temperature different at night the phenomenon is still obvious. Therefore, in our opinion, the temperature different of the air is not a necessary condition of “ the false water puddle on the tarmac.” We bring up the model to explain the phenomenon that when the incident angle of the light approach 90 degrees, the light will result in one-way reflection. According to the model, furthermore, we make experiments at midnight and at dawn. The result of the experiment assures us the hypothesis of the model, Consequently, we hold the ideal that the main condition of the “false water puddle on the tarmac.” Is not because of the refraction and the total reflection but because the light reflects off the road and result in the one-way reflection on the tarmac road.
一些Moire patterns 的數學性質研究
Moire 為法文，其英譯為watered， 是古代織布技術的一種應用；將印有規律條?的透明薄片重疊時，稍微移動或轉動其中的一片，會形成極大的圖形變化，稱為moire pattern本作品針對三個moire pattern 的數學式加以推導：(一)、兩張透明片各印有等間隔平行線，轉動其中一片使兩線的夾角θ，亮紋垂直距離和暗?垂直距離的比值為tanθ/2tanθ 。(二)、兩張透明片各印有輻射線，重疊後行成圓系，可由代數或幾何加以證明，利用三角函數可推導出此圓系方程式為：x2+{y-rtan[π/2-(θ-?)]}2)]}={rsec[π/2-(θ-?)]}2)]}\r \r (三)、透明片A 印有等間隔平行線，B 印有符合高斯曲線的平行線，AB 重疊時，形成一系列的高斯曲線，AB 的夾角減少時，會增大曲線的曲率，我們進一步討論曲線的曲率和平行線斜率的關係。Moire is the French word “watered” and refers to an ancient technique employed in cloth making. The moire occurs whenever two or more transparent sheets with periodic strips on them are superposed. The characteristic of moire patterns is the fact that a slight shift of sheets will create dramatic alternations in the observed patterns. In the present report, We derive the equations of three different moire patterns. First of all, take a sheet with equal spaced straight lines and placed it on top of another identical sheet. They are made to intersect and form an angle of θ. As the angle changes slightly, it produces huge changes in the spacing of moire fringes. We can derive a formula related to the interfringe distance. The ratio of bright fringes and dark fringes is tanθ/2tanθ.Secondly, two transparent sheets with radial lines on them are overlapped, forming a pattern similar to the lines of force between point charges. We can find that the pattern is a series of circle by means of algebraic and geometric proofs. And proven by trigonometric functions, we canconclude that they satisfy the equation :x2+{y-rtan[π/2-(θ-?)]}2)]}={rsec[π/2-(θ-?)]}2)]}\r Thirdly, a set of lines of equal spacing is overlapped with a second set of lines whose spacing are derived from a Gaussian curve. A series of Gaussian curves is reproduced in a moire pattern. Reducing the angle of intersection between the two figures steepen the curvature. We discussed the relation between the curvature and the slope of inclined lines.
聚球藻 RF 一 1 品系生物時鐘之特性
我們成功的用溶氣計偵測到了聚球藻 RF-1 在 28℃下光合作用的概日韻律。和傳統的研究方法比起來，這個方法具有連續偵測的優點，減少因不斷取樣所造成的影響，此實驗可觀察到聚球藻 RF-1 溶氣量之變化圖與一般藻類（如單殼縫藻）不同.在光 /暗條件下 RF-1 之溶氣量的增加與減少均呈週期性變化，而且此變化現象在進入連續照光後仍然可以維持兩個循環以上，這些結果顯示以溶氣計連續偵測聚球藻 RF -1之概日韻律是可行的，而且所得到的變化圖形遠比傳統方法（於不同時間取樣）所得者自然。本實驗同時發現含聚球藻之培養液的溫度，在進入黑暗週期時會有明顯的上升，由於其變化程度比其他藻類明顯，如加以探討應有助於對此藻以及其韻律特性之瞭解。We successfully detected the photosynthesis circadian rhythm of the prokaryote Synechococcus RF-1 under 28℃ by a DO (Dissolved-Oxygen) meter. The advantage of this method, comparing with the traditional methods, is that it can detect signals continuously, reduce the influence of discrete sampling. The DO curves of the Synechococcus RF-1 are different from that of other algae. Under Light/Dark conditions, the DO values of RF-i increased and decreased periodically. The periodic phenomena progressed over two cycles under constant lighting conditions. These results revealed the feasibility of using DO meter to continuous detect the circadian rhythm of the Synechococcus RF-1 The detected DO curves looked more natural than those obtained in the traditional discrete-sampling method. We also found that the temperature of the culture increased in dark cycle. Since the variation is clearer than that of other algae, further investigation will benefit the understanding of the Synechcoccus RF-i and its circadian rhythm.