✏️ Rules for Drawing Ray Diagrams | 繪畫光線圖的法則

• Ray 1 (Parallel Ray): A ray parallel to the principal axis…
  Convex: is refracted through the principal focus (\( F \)) on the other side. (凸透鏡：折射後穿過另一側的主焦點。)
  Concave: is refracted such that it appears to diverge from the principal focus (\( F \)) on the same side. (凹透鏡：折射後看似從同一側的主焦點發散出來。)


• Ray 2 (Centre Ray): A ray passing through the optical centre (\( C \)) travels straight on without deviation for both types of lenses. (穿過光心的光線，無論凸透鏡或凹透鏡，皆直線傳播不偏折。)


• Ray 3 (Focal Ray):
  Convex: A ray passing through the focus (\( F \)) is refracted parallel to the principal axis. (凸透鏡：穿過焦點的光線，折射後平行於主軸。)
  Concave: A ray heading towards the focus (\( F \)) on the opposite side is refracted parallel to the principal axis. (凹透鏡：射向另一側焦點的光線，折射後平行於主軸。)

🔍 Convex Lens (凸透鏡)

As the object moves closer to the lens from infinity, the image moves further away and becomes larger. 當物體從無限遠移近透鏡時，影像會移遠並變大。

• \( u > 2f \): Real, inverted, diminished. (e.g., Camera) 實像、倒立、縮小。(如：相機)
• \( u = 2f \): Real, inverted, same size. 實像、倒立、等大。
• \( f < u < 2f \): Real, inverted, magnified. (e.g., Projector) 實像、倒立、放大。(如：投影機)
• \( u = f \): Image at infinity. 影像在無限遠。
• \( u < f \): Virtual, erect, magnified. (e.g., Magnifying glass) 虛像、正立、放大。(如：放大鏡)

👓 Concave Lens (凹透鏡)

No matter where the object is placed, a concave lens always forms an image with the same properties: 無論物體放在哪裡，凹透鏡總是形成相同性質的影像：

• Always: Virtual, erect, and diminished. 必定是：虛像、正立、縮小。
• The image is always located between the object and the lens. 影像總是在物體和透鏡之間。

Distant Object Method | 遠物法 (For Convex Lenses)

1. Point the convex lens at a distant object (e.g., a distant building or window). 將凸透鏡對準遠處的物體 (如遠處的建築物或窗戶)。
2. Place a white screen behind the lens. 在透鏡後方放置一個白底屏幕。
3. Adjust the distance between the lens and the screen until a sharp, inverted image of the distant object is formed on the screen. 調整透鏡與屏幕之間的距離，直到屏幕上形成清晰的倒立影像。
4. Measure the distance between the lens and the screen. This distance is approximately equal to the focal length (\( f \)). 量度透鏡與屏幕之間的距離。此距離約等於焦距 (\( f \))。

Reason: Rays from a distant object are almost parallel. Parallel rays converge at the focal point. 原因：來自遠處物體的光線幾乎是平行的。平行光會聚於焦點。

🔎 Magnifying Glass | 放大鏡

A magnifying glass is simply a convex lens. To use it, the object must be placed closer than the focal length (\( u < f \)). This produces a virtual, erect, and magnified image on the same side as the object. 放大鏡就是一個凸透鏡。使用時，物體必須放在焦距之內 (\( u < f \))。這會產生一個虛擬、正立且放大的影像。

👁️ Corrective Lenses for Vision | 視力矯正透鏡

• Short-sightedness (Myopia) | 近視: The eyeball is too long or the lens is too thick, causing distant objects to focus in front of the retina.
  Correction: Use a Concave Lens to diverge the rays before they enter the eye. (矯正：使用凹透鏡使光線在進入眼睛前發散。)


• Long-sightedness (Hypermetropia) | 遠視: The eyeball is too short or the lens is too thin, causing near objects to focus behind the retina.
  Correction: Use a Convex Lens to converge the rays before they enter the eye. (矯正：使用凸透鏡使光線在進入眼睛前會聚。)


• Old Sight (Presbyopia) | 老花: The eye lens loses its elasticity due to aging, making it difficult to focus on near objects.
  Correction: Use a Convex Lens (often as reading glasses or bifocals) to help converge light from near objects. (矯正：使用凸透鏡（常見於老花眼鏡或雙光鏡）幫助會聚近處物體的光線。)