Physics 光學問題

1. 為什麼 refractive index = real depth/ apparent depth ? 可否證明一次？
呢題真係好難淨靠文字講,我都懶得畫出黎,直接比條link.
http://www.physicstutorials.org/home/optics/refraction-of-light/the-laws-of-refraction/73-apparent-depth-real-depth
你可能會問,點解sinθ=tanθ,比多條link你:http://en.wikipedia.org/wiki/Small-angle_approximation By identity, sinθ=θ=tanθ ∴sinθ=tanθ
咁你繼續睇落去就明架啦:D

2. 色散的原理是什麼？ （白光進入三菱鏡後分散成紅到紫光）
老師說 色散的原因是不同顏色的光速度不同，但是它們不都是 3*10^8 m/s 嗎？
這是否和波長和頻率有關？ 可否解釋一次？
係冇錯,你睇番成個em spectrum,可以知道visible spectrum頭尾係infra-RED同埋ultra-VIOLET,就係visible spectrum最頭頭尾個兩隻顏色,只不過紅外線同紫外線係我地睇唔到姐,anyway,其實重點係IN VACUUM(真空),所有EM WAVES係3*10^8m/s,但經過唔同medium(唔計air),佢地個速度會變.By v=λf(如果你未學過可以上google睇),frequency(f) is constant, wavelength(λ) decreases,所以v decreases,慢D,自然bend多D,至於點解有色散,係因為本身佢地嘅energy level唔同,所以v decreases 幾多唔係七隻顏色都一樣,所以先有似散左七色光咁(其實唔係太重要你可以無視,學多當增潤
3.由於折射的關係，我們會覺得水中的物件比較淺，（real depth > apparent depth） ，但是apparent depth 是否一定在 real depth 的正上方？可否在 左上方或右上方？ 如何證明？
呢個問題我讀都冇諗過,好問題一個.其實我真係唔識答XD

為什麼白光進入三菱鏡後會有色散，而白光進入其他介質（例如水，玻璃）又不會？
其實會,不過細到睇唔到,(玻璃明顯D,你試下"控"埋D塊玻璃邊睇,你會見到有紅綠藍嘅野,其實已經係(我諗)) 不過我覺得另外一個可信D嘅原因係,光經過三菱鏡嗰時有折射兩次,令到個折射幅度大左,七隻色分開得明顯,就唔只係望到三原色.

2014-09-15 22:49:58 補充：
第一題個θ係in radian, not in degree.
單位轉換: 1 rad = 180/π degree
至於點解要用呢個system你可以好奇查下,我遲D諗到再補第三題
Btw學M2野有幫助(calculus)

1. You may refer to the proof given in the following web-page:

http://www.physicstutorials.org/home/optics/refraction-of-light/apparent-depth-real-depth

2. Your teacher is right. The speed of light of 3 x 10^8 m/s is the speed at vacuum. In a medium, light of different frequencies have different speeds. In general, the higher the frequency of light, the lower is the speed in a medium.

Dispersion (色散) also occurs when white light enters glass, water and other media. Dispersion is observed to be more prominent in a prism due to the higher refractive index of the prism material.

3. For water, real depth > apparent depth. This relation is true for substances with refractive index > 1.

You observe that the image of an object is shallower in water and directly above the object is only true when you are looking vertically downward onto the object. Should you observe the object obliquely, you would see it displaced laterially.

為什麼白光進入三菱鏡後會有色散，而白光進入其他介質（例如水，玻璃）又不會？

當然會，你沒見過彩虹嗎? 彩虹一現，好多人就會舉機拍照。