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2026年9月20日星期日

Calculation of aperture

The f-number scale increases by multiples of
2the square root of 2 end-root
(approximately 1.414)
because doubling or halving the light entering the camera requires doubling or halving the area of the circular aperture, not its diameter.

Here is the simple mathematical breakdown of why this happens:

1. Light and Area
The amount of light that passes through a lens depends entirely on the area (A) of the optical opening. Since the aperture is a circle, its area is calculated using the formula:

This shows that the area (
Acap A
) is proportional to the square of the diameter (
D2cap D squared
)
.

2. The Inverse Relationship
From your previous formula, the diameter is
. This means the f-number (
Ncap N
) is in the denominator.
  • To let in half the light, you need half the area.
  • To get half the area, you must reduce the diameter by a factor of
    2the square root of 2 end-root
    .
  • Because
    Ncap N
    is inversely proportional to
    Dcap D
    , you must multiply the f-number by
    2the square root of 2 end-root
    to make the opening smaller by that exact ratio.
Google Gemini

Let 焦距 (f) be 35 mm and F值 (N) = 2

光圈孔直徑 (D) = f / N

D = 35 mm ÷ 2 = 17.5 mm

A = 3.1416 * 8.75mm * 8.75mm = 240.5 mm square

0.5 A = 3.1416  * r * r = 120.3 mm square

r * r = 38.3 mm square

r = 6.2 mm

Original diameter is 17.5mm
Area in half, new diameter is 12.4mm

D = f / N
12.4 = 35 / N
N = 2.8

2026年9月17日星期四

Main Uses of Microsoft PowerToys

1. Window & Workspace Management

  • FancyZones: Create custom window layouts (grids, columns, multi‑monitor setups) for efficient multitasking.

  • Always on Top: Pin a window above others with a shortcut.

  • Crop and Lock: Turn part of a window into a separate interactive thumbnail.

  • Grab and Move: Resize/move windows by dragging anywhere inside them with a modifier key.

2. File & Explorer Enhancements

  • PowerRename: Bulk rename files with regex or case conversion.

  • Image Resizer: Right‑click images to resize in batches.

  • File Explorer Add‑ons: Preview pane support for SVG, Markdown, PDF, and more.

  • File Locksmith: See which processes are locking a file.

  • Peek: Preview file contents instantly without opening apps.

3. Keyboard & Input Tools

  • Keyboard Manager: Remap keys or create custom shortcuts system‑wide.

  • Text Extractor (OCR): Copy text from images, PDFs, or dialogs.

  • Quick Accent: Type accented characters easily.

4. Mouse & Display Utilities

  • Find My Mouse: Highlight cursor with a double‑tap of Ctrl.

  • Mouse Highlighter & Crosshairs: Useful for presentations.

  • Power Display: Control monitor brightness, contrast, and input source.

  • Mouse Without Borders: Use one keyboard/mouse across multiple PCs.

5. System & Workflow Tools

  • PowerToys Run (Alt+Space): Instant launcher for apps, files, commands, and calculations.

  • Awake: Keep PC awake without changing system sleep settings.

  • Hosts File Editor: Manage domain/IP mappings.

  • Environment Variables Manager: Organize profiles for development.

  • Light Switch: Auto switch between light/dark themes.

  • Command Not Found: Suggests WinGet packages when a PowerShell command fails.

Microsoft Copilot

2026年9月16日星期三

Achilles tendon

Achilles:希臘英雄阿基里斯(Achilles),他全身刀槍不入,唯獨腳踝是弱點。

是人體最強壯、最厚的腱,但也容易受傷(例如運動員的「阿基里斯腱斷裂」)。

Microsoft Copilot

Keep yourself busy

if somebody/something works or happens in tandem with somebody/something else, they work together or happen at the same time

The Central Executive Network (CEN), also called the Frontoparietal Network, is a large‑scale brain system responsible for executive functions like working memory, decision‑making, and goal‑directed behavior. It is mainly anchored in the dorsolateral prefrontal cortex and posterior parietal cortex. 

ponder: to think about something carefully for a period of time

see-saw:  a piece of equipment for children to play on consisting of a long flat piece of wood that is supported in the middle. A child sits at each end and makes the see-saw move up and down.

The Salience Network (SN) is a core brain system that acts like a “switchboard,” helping you detect important internal and external stimuli and decide whether to engage the Default Mode Network (DMN) or the Central Executive Network (CEN).

salience: ​the quality of being particularly important or easy to notice

revert to something: to return to a former state; to start doing something again that you used to do in the past

dismantle something: to end an organization or a system gradually in an organized way

Emerging evidence means new, freshly uncovered, or developing facts and data that support a specific trend, hypothesis, or shift in clinical, scientific, or social understanding.

render: to cause somebody/something to be in a particular state or condition

vivid: (of memories, a description, etc.) producing very clear pictures in your mind

utmost: greatest; most extreme

unapologetically: without saying or showing that you are sorry about something, even in situations in which other people might expect you to

notable: deserving to be noticed or to receive attention; important

confines: limits or borders

Nicole Vignola "Rewire"

hk.dictionary.search.yahoo.com

oxfordlearnersdictionaries.com

dictionary.cambridge.org

Microsoft Copilot

Dreaming again

Canon EOS R8 Mark II is an entry level camera. RF 24‑105mm f/4L is a luxury lens. Although lens is more important than body, is it worthwhile to buy a luxury lens for an entry level camera?

This is a really thoughtful question — and it touches on one of the most debated topics in photography: is it better to invest in the lens or the body?

Lens importance: The lens defines sharpness, contrast, color rendering, and bokeh. A high‑quality lens like the RF 24‑105mm f/4L IS USM will deliver professional‑grade results even on an entry‑level body.

Body importance: The camera body contributes sensor performance, autofocus speed, ergonomics, and video features. But bodies evolve quickly — today’s “entry‑level” R8 Mark II already has IBIS, advanced AF, and strong video specs.

Yes, it’s worthwhile if you see photography as a long‑term pursuit. The lens will outlast the body and can move with you when you upgrade to R6 Mark III or R7 later.

No, it’s less worthwhile if budget is tight and you mainly shoot casual travel or family photos — in that case, the RF 24‑105mm STM (~395g, cheaper) gives good results without overspending.

Canon EOS R8 Mark II body is indeed lighter than the RF 24‑105mm f/4L IS USM lens. The center of gravity shifts forward. This is common with mirrorless cameras, since bodies are designed to be compact while pro lenses remain substantial.

Balance: You’ll feel the weight in your left hand supporting the lens, not in the grip. A wrist strap or tripod helps for long sessions.

Image quality: The L‑series optics more than compensate for the imbalance — sharper, better contrast, weather‑sealed.

Microsoft Copilot

2026年9月15日星期二

太空軍備競賽

The U.S. Space Force just made history: Air Force Secretary Troy Meink publicly confirmed for the first time that the U.S. has deployed on-orbit space weapons to defend against hostile adversaries. This marks a major shift in U.S. military transparency and could accelerate an arms race in space.

adversary: a person that somebody is opposed to and competing with in an argument or a battle

Microsoft Copilot

www.oxfordlearnersdictionaries.com

Prime lens

大光圈定焦鏡雖然提升低光能力,但景深淺、只能把焦點放在某一位置、背景會模糊。

攝影時的直接調整(最推薦先嘗試)

  • 縮小光圈:把 f/2 改為 f/2.8 f/4 可顯著增加景深。若光線不足,可同步提高 ISO 或放慢快門(注意手持極限)。適用於可控制曝光或靜態場景。
  • 拉遠距離 / 改變構圖:把相機往後退、或讓被攝體離背景更近/遠,能改變景深感與背景模糊程度。這是最不破壞畫質的方式。

大光圈定焦鏡提供的是「畫面語言與光學特性」而非單純的曝光補償。

低光手持能力:即使有三腳架,很多場景需要手持快速反應(街拍、活動),大光圈能讓你用更低 ISO 或更快快門。

創作限制促進進步:定焦限制你移動與構圖,反而能鍛鍊視覺判斷與主題處理。

體積與重量:某些大光圈定焦比高端變焦更輕便,長時間外拍更省力。

Microsoft  Copilot

Anatomy of a class

In Python, instance attributes are variables that belong to a specific object created from a class. They are usually defined inside the __init__ method using self, and each object has its own independent copy of these attributes. This makes them different from class attributes, which are shared across all instances.

class Car:

    def __init__(self, brand, model):

        # Instance attributes

        self.brand = brand

        self.model = model


car1 = Car("Toyota", "Camry")

car2 = Car("Honda", "Civic")


print(car1.brand, car1.model)  # Toyota Camry

print(car2.brand, car2.model)  # Honda Civic


class Dog:
    def __init__(self, name):
        self.name = name
        self.legs = 4
    
    def speak(self):
        print(self.name + ' says: Bark!')

myDog = Dog('Rover')
print(myDog.name)
print(myDog.legs)

Class Definition
You define a class Dog with an __init__ method and a speak method.

__init__ Method
Runs automatically when you create a new Dog object.
self.name = name → assigns the given name to the instance.
self.legs = 4 → every dog object starts with 4 legs.

Instance Attributes
self.name and self.legs are instance attributes.
Each Dog object has its own copy of these attributes.

Creating an Object
myDog = Dog('Rover') → creates a new Dog instance with name = "Rover" and legs = 4.

Accessing Attributes
print(myDog.name) → prints "Rover".
print(myDog.legs) → prints 4.

Method Usage
If you call myDog.speak(), it will print:
Rover says: Bark!

adorable: very attractive and easy to feel love for

Static attributes in Python are what we usually call class attributes. Unlike instance attributes (unique to each object), static/class attributes are shared across all instances of the class. They are defined directly inside the class body, not inside __init__.

connotation: ​an idea suggested by a word in addition to its main meaning

In Python, a getter function is a method that allows you to safely access (or "get") the value of an attribute from a class. It’s often used together with properties to control how attributes are read, especially when you want to add validation, formatting, or encapsulation.

Encapsulation in Python is the practice of bundling data (attributes) and the methods (functions) that operate on that data into a single unit, typically a class. Its primary goal is to hide internal implementation details and restrict direct access to an object's state to prevent accidental modifications.

class Dog: _legs = 4 # static/class attribute def __init__(self, name): self.name = name # instance attribute def getLegs(self): # getter function return self._legs def speak(self): print(self.name + ' says: Bark!') myDog = Dog('Rover') print(myDog.name) # Rover print(myDog.getLegs()) # 4


In your example, you’ve introduced a static (class) attribute _legs and a getter function getLegs() to access it.

Static/Class Attribute (_legs)
Defined directly in the class body (_legs = 4).
Shared across all Dog objects.
Accessible via Dog._legs or through an instance (myDog._legs).

Instance Attribute (name)
Defined inside __init__ using self.name.
Unique to each object (e.g., Rover, Buddy, Max).

Getter Function (getLegs)
Provides controlled access to the static attribute.
Returns self._legs, which refers to the class-level _legs.

myDog = Dog('Rover') myDog._legs = 3 print(myDog.name) print(myDog.getLegs()) print(Dog._legs)

Class Attribute _legs = 4
Defined at the class level.
Shared by all Dog objects unless shadowed.

Instance Creation
myDog = Dog('Rover') → creates a new dog with name = "Rover".
At this point, myDog sees _legs from the class (Dog._legs = 4).

Assigning myDog._legs = 3
This does not change the class attribute.
Instead, it creates a new instance attribute _legs on myDog only.
Now myDog has its own _legs = 3, shadowing the class’s _legs.

Printing Values
print(myDog.name)"Rover" (instance attribute).
print(myDog.getLegs())3 (because self._legs now refers to the instance attribute).
print(Dog._legs)4 (class attribute remains unchanged).

Microsoft Copilot

避免重複負面的言論

grab: to take or hold somebody/something with your hand suddenly or roughly

zesty: ​that tastes or smells sharp and fresh

compel: to force somebody to do something; to make something necessary

perpetuate: to make something such as a bad situation, a belief, etc. continue for a long time

gasp: to take a quick deep breath with your mouth open, especially because you are surprised or in pain

Our words shape the way we think, and the way we think shapes how we feel; how we feel determines what we do, and what we do determines our belief.

這句話說明一個循環因果:我們的語言(說的話)會影響思維方式,而思維方式又會影響情緒;情緒決定行為,行為反過來形塑信念。換言之,語言 → 思考 → 感受 → 行為 → 信念,任何一環的改變都會影響整個自我認知與世界觀。

minute: tiny

Mind wandering is the natural drifting of your attention away from an external task and toward your internal thoughts and daydreams.

The Default Mode Network (DMN) is a large-scale brain system most active when you’re not focused on external tasks—such as during daydreaming, self-reflection, or imagining the future. It plays a central role in constructing your sense of self, but disruptions in its activity are linked to conditions like Alzheimer’s, depression, and autism.

Metacognition is the ability to think about your own thinking—monitoring, evaluating, and regulating how you learn, remember, and solve problems. It is central to effective learning, decision-making, and self-awareness.

Self-referential thinking is a cognitive process where you relate neutral external events, information, or stimuli directly to yourself.

underscore: to emphasize or show that something is important or true

sift: to examine something very carefully in order to decide what is important or useful or to find something important

Nicole Vignola "Rewire"

hk.dictionary.search.yahoo.com

oxfordlearnersdictionaries.com

Google AI overview

Explained by Microsoft Copilot

Moon and Venus


2026年9月14日星期一

技術的訓練比器材更重要

Canon EOS 1500D

  • 1500D 是 Canon 入門級 DSLR,24.1MP APS‑C 感光元件,對新手來說解析力充足,日常、旅行、人像都夠用。

  • 有完整的 P/Av/Tv/M 模式、內建閃燈、9 點 AF 與場景模式,很適合由自動過渡到半自動(Av/Tv)再到全手動(M)。

  • 限制主要是對焦速度、連拍與高 ISO 表現不如新機,但作為「學習機」完全合格。

EF‑S 18–135mm f/3.5–5.6 IS USM(旅遊/日常一鏡)

  • 覆蓋廣角到中長焦(APS‑C 等效約 29–216mm),非常適合旅行、風景、街拍、家庭照。

  • IS 防手震對新手很友善,能提升手持成功率,尤其在室內或傍晚。

  • 限制是最大光圈隨焦段變化(f/3.5–5.6),弱光與背景虛化能力不如定焦大光圈。

EF 35mm f/2 IS USM(二手定焦)

  • 在 APS‑C 上等效約 56mm,接近「標準視角」,非常適合人像、街拍、室內。

  • f/2 大光圈能帶來明顯的背景虛化與更好的弱光表現,是學習「景深控制」的好鏡頭。

  • 有 IS 的 35mm f/2 在 Canon EF 定焦中很少見,手持慢速快門更安心。

這套裝備的優勢(對新手)

  • 一變焦 + 一定焦,剛好練習兩種思維:

    • 用 18–135mm 學習構圖、焦段選擇、旅行隨拍。

    • 用 35mm f/2 練習「用腳變焦」、控制景深、弱光拍攝。

  • 兩支都有 IS,對新手手持成功率很友好。

可能的限制與升級路線(先不用急)

  • 高 ISO 噪點與對焦速度:1500D 在很暗環境會比較吃力,但你可以用三腳架、補光或放慢快門來補。

  • 背景虛化極限:35mm f/2 已不錯。

  • 若你之後想轉無反(如 Canon R 系列),EF 鏡可透過轉接環繼續用,不會浪費。

給你的練習建議(配合現有器材)

  • 先用 Av 模式:

    • 35mm f/2:光圈設 f/2–2.8 拍人像/靜物,練習對焦點與景深。

    • 18–135mm:白天設 f/5.6–8 拍風景/建築,練習構圖與焦段選擇。

  • 嘗試同一場景用不同焦段(例如 35mm vs 50mm 等效)拍,比較視角與背景壓縮感。

  • 每週設定一個小主題:例如「只用 35mm f/2 拍一週」或「只用 18–135mm 的 50mm 端」。


腳架是提升畫質與創作自由的關鍵工具。你已有 1500D + 18–135mm + 35mm f/2,配上鋁合金腳架,可以這樣善用:

一、先把腳架「用穩」

  • 先伸展較粗的腳管,最後才伸最細那節;盡量少用最細那節以提升穩定性。

  • 在戶外盡量把中軸降到最低(不要拉很高),重心越低越穩。

  • 雲台鎖緊順序:先鎖腳管→再鎖雲台→最後微調構圖;拍攝前輕按機身確認不會晃。

二、相機設定:腳架專屬套路

  • 關 IS:18–135mm 與 35mm f/2 都有 IS,但上腳架時建議把 IS 關掉,避免防抖系統自己「微震」。

  • 用 2 秒自拍或遙控快門:避免按快門時震動;1500D 有 2 秒倒數,很實用。

  • 關「長時間曝光降噪」除非你真的需要(會拖慢拍攝節奏)。

  • 格式:若你願意後製,建議 RAW;若只想直出,Fine JPEG 也可以。

三、最適合腳架的練習題材(配合你的鏡頭)

1) 夜景與長曝光(城市、車軌、光繪)

  • 鏡頭:18–135mm 收至 f/8–11,ISO 100。

  • 模式:M 或 Tv,快門 2–30 秒試拍;用 2 秒自拍。

  • 重點:腳架讓你在低 ISO 下用慢快門,畫面更乾淨、動態範圍更好。

2) 日落/藍調時段風景

  • 鏡頭:18–135mm 廣角端(18–24mm)拍大場景;或 35mm f/2 拍局部。

  • 光圈:f/8–11 保證前後都清晰;ISO 100。

  • 技巧:用腳架鎖定構圖,等光線變化連拍,之後可選最佳一張或做合成。

3) 靜物/室內弱光(食物、小物件、家居)

  • 鏡頭:35mm f/2 很適合;腳架讓你用 f/2–2.8 仍不怕手震。

  • 設定:Av 模式,光圈 f/2–4,ISO 100–400,讓快門自然變慢。

  • 好處:可以用更低 ISO、更細膩的畫質,同時精確控制景深。

4) 多重曝光/合成(進階但很好玩)

  • 固定腳架位置,連拍多張:

    • 曝光包圍(不同亮度)→ 後製合成 HDR。

    • 不同對焦距離 → 後製景深合成(微距/近攝很有用)。

  • 腳架確保每張構圖一致,合成更乾淨。

四、把腳架變成「學習工具」

  • 慢快門練習:刻意用 1/4 秒、1 秒、4 秒等不同快門,觀察動態模糊效果。

  • 精準構圖:腳架固定後,你可以慢慢調整水平線、前景比例、三分法。

  • 自拍與合照:家人朋友合照、或把自己放進畫面(用 2 秒/10 秒倒數)。

五、外出使用小技巧

  • 地面不平時:先調兩隻腳,再用第三隻微調;盡量不用中軸升降來「硬撐」。

  • 風大:背包掛中軸、身體擋風、快門用 2 秒倒數。


Perplexity.AI