【2027 DSE】Physics 波動 Wave Motion 公式全攻略：常見失分位一次睇晒

波速、頻率與週期

★ v = f λ

★ T = 1 / f

連繫波速、頻率、波長及週期；跨越靜止介面時，頻率由波源決定。

Relate wave speed, frequency, wavelength and period. Frequency stays fixed by the source across a stationary boundary.

折射時不要把頻率也改變；時間圖讀週期，距離圖讀波長。

Do not change frequency during refraction. Read period from a time graph and wavelength from a distance graph.

折射定律

★ n = sin i / sin r

★ n₁ sin θ₁ = n₂ sin θ₂

★ n = c / v

第一式用於由空氣（折射率近似 1）進入介質；一般兩介質用第二式。角度均由法線量起。

The first form is for light entering a medium from air with index approximately 1. Use the second form between general media; measure angles from the normal.

不能從表面量角；一般情況下，sin θ₁ / sin θ₂ 是 n₂ / n₁。

Do not measure angles from the surface. In general, sin θ₁ / sin θ₂ equals n₂ / n₁.

臨界角與全內反射

★ sin C = 1 / n

★ sin C = n₂ / n₁

由較高折射率 n₁ 射向較低折射率 n₂；第一式的外界是空氣。入射角大於 C 才發生全內反射。

Light must travel from higher n₁ to lower n₂. The first form assumes air outside. Total internal reflection occurs for incidence greater than C.

由低折射率射向高折射率不會全內反射；入射角等於臨界角時，折射角是 90°。

There is no total internal reflection from lower to higher index. At the critical angle, refraction is at 90°.

薄透鏡

1 / u + 1 / v = 1 / f

求單一薄透鏡的物距、像距及焦距；採用「實為正」慣例。

Relate object distance, image distance and focal length for a single thin lens, using the real-is-positive convention.

虛像的像距為負；發散透鏡的焦距為負。此處 u、v 是距離，不是速度。

A virtual image has negative image distance; a diverging lens has negative focal length. Here u and v are distances, not velocities.

透鏡放大率（大小）

★ M = |h_i / h_o| = |v / u|

比較像與物的高度大小；這裏 M 定義為非負的放大率大小。

Compare image and object heights; M here is the non-negative magnitude of magnification.

M 大於 1 只表示放大，不能單憑大小判斷正立、倒立或虛實。

M greater than 1 means enlarged; magnitude alone does not determine orientation or whether the image is real.

干涉：程差

★ Δx = m λ

★ Δx = (m + ½) λ

兩相干、同相波源：第一式為相長干涉，第二式為相消干涉；m = 0, 1, 2, …。

For coherent in-phase sources, the first condition gives constructive and the second destructive interference; m = 0, 1, 2, ….

程差是兩條傳播路徑長度之差，不是波源間距；反相波源的條件須對調。

Path difference is the difference between travel distances, not source separation. The conditions swap for antiphase sources.

駐波的長度關係

★ 相鄰波節距離 = λ / 2

★ 波節至相鄰波腹距離 = λ / 4

★ L = n λ / 2

從駐波圖讀波長；第三式適用於兩端均為波節的弦，n 為波腹數（正整數）。

Read wavelength from a stationary-wave pattern. The third relation applies to a string with nodes at both ends; n counts antinodes.

相鄰波節相距半個波長，不是一個波長；先確認兩端的邊界條件。

Adjacent nodes are half a wavelength apart, not one wavelength. Check the end conditions first.

楊氏雙縫干涉

Δy = λ D / a

雙縫間距 a、至屏距離 D；在遠屏及小角度近似下，求相鄰亮紋或暗紋的間距。

For a double slit of separation a and a distant screen at D, find adjacent bright- or dark-fringe spacing under the small-angle approximation.

不要把雙縫公式直接套用於光柵；a 是雙縫間距，不是單縫寬度。 [R3]

Do not apply the double-slit formula directly to a diffraction grating. Here a is slit separation, not slit width.

衍射光柵

d sin θ = n λ

★ d = 1 / ℓ

正入射光柵，求第 n 級主極大方向；ℓ 為每單位長度的刻線數，d 為相鄰刻線間距。

For normal incidence, find the nth principal maximum. ℓ is the number of lines per unit length and d the line spacing.

刻線數若以每毫米表示，須先換成每米；最高級數必須是滿足 sin θ ≤ 1 的整數。

Convert lines per millimetre to lines per metre. The highest order must be an integer satisfying sin θ ≤ 1.

回聲測距

★ d = v t / 2

聲源與反射面位置不變，t 是聲波發出至回聲返回的總時間，d 是單程距離。

For a stationary source and reflector, t is the round-trip echo time and d the one-way distance.

回聲來回走了兩程；忘記除以 2 會把距離加倍。 [R12]

An echo travels out and back. Omitting the factor of 2 doubles the distance.