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Physics Formula Sheet

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Please Do Not Write on This Sheet
Physics Formula Sheet
Chapter 1: Introduction: The
Nature of Science and Physics
π‘₯=
𝑅𝑦 = 𝐴𝑦 + 𝐡𝑦
𝑅 = √𝑅π‘₯2 + 𝑅𝑦2
−𝑏 ± √𝑏 2 − 4π‘Žπ‘
2π‘Ž
π‘…π‘Žπ‘‘π‘–π‘’π‘  π‘œπ‘“ πΈπ‘Žπ‘Ÿπ‘‘β„Ž = 6.38 × 106 π‘š
π‘€π‘Žπ‘ π‘  π‘œπ‘“ πΈπ‘Žπ‘Ÿπ‘‘β„Ž = 5.98 × 1024 π‘˜π‘”
𝑐 = 3.00 × 108 π‘š/𝑠
π‘π‘š2
𝐺 = 6.673 × 10−11
π‘˜π‘”2
𝑁𝐴 = 6.02 × 1023
π‘˜ = 1.38 × 10−23 𝐽/𝐾
𝐽
𝑅 = 8.31 ⁄π‘šπ‘œπ‘™ ⋅ 𝐾
𝜎 = 5.67 × 10−8 π‘Š/(π‘š2 ⋅ 𝐾)
π‘˜ = 8.99 × 109 𝑁 ⋅ π‘š2 /𝐢 2
π‘žπ‘’ = −1.60 × 10−19 𝐢
πœ–0 = 8.85 × 10−12 𝐢 2 /(𝑁 ⋅ π‘š2 )
πœ‡0 = 4π × 10−7 𝑇 ⋅ π‘š/𝐴
β„Ž = 6.63 × 10−34 𝐽 ⋅ 𝑠
π‘šπ‘’ = 9.11 × 10−31 π‘˜π‘”
π‘šπ‘ = 1.6726 × 10−27 π‘˜π‘”
π‘šπ‘› = 1.6749 × 10−27 π‘˜π‘”
π‘Žπ‘šπ‘’ = 1.6605 × 10−27 π‘˜π‘”
π‘˜π‘”
𝐷𝑒𝑛𝑠𝑖𝑑𝑦 π‘œπ‘“ π‘€π‘Žπ‘‘π‘’π‘Ÿ = 1000 3
π‘š
Chapter 2: Kinematics
π›₯π‘₯ = π‘₯𝑓 − π‘₯0
π›₯𝑑 = 𝑑𝑓 − 𝑑0
π›₯π‘₯ π‘₯𝑓 − π‘₯0
𝑣=
=
π›₯𝑑
𝑑𝑓 − 𝑑0
π›₯𝑣 𝑣𝑓 − 𝑣0
π‘Ž=
=
π›₯𝑑
𝑑𝑓 − 𝑑0
π‘₯ = π‘₯0 + 𝑣𝑑
𝑣0 + 𝑣
𝑣=
2
𝑣 = 𝑣0 + π‘Žπ‘‘
1
π‘₯ = π‘₯0 + 𝑣0 𝑑 + π‘Žπ‘‘ 2
2
𝑣 2 = 𝑣02 + 2π‘Ž(π‘₯ − π‘₯0 )
π‘š
𝑔 = 9.80 2
𝑠
Chapter 3: Two-Dimensional
Kinematics
𝐴π‘₯ = 𝐴 π‘π‘œπ‘  πœƒ
𝐴𝑦 = 𝐴 𝑠𝑖𝑛 πœƒ
𝑅π‘₯ = 𝐴π‘₯ + 𝐡π‘₯
πœƒ = π‘‘π‘Žπ‘›−1
𝑅𝑦
𝑅π‘₯
2
𝑣0𝑦
2𝑔
2
𝑣0 𝑠𝑖𝑛 2πœƒ0
𝑅=
𝑔
𝑣π‘₯ = 𝑣 π‘π‘œπ‘  πœƒ
𝑣𝑦 = 𝑣 𝑠𝑖𝑛 πœƒ
β„Ž=
𝑣 = √𝑣π‘₯2 + 𝑣𝑦2
πœƒ = π‘‘π‘Žπ‘›−1
𝑣𝑦
𝑣π‘₯
Chapter 4: Dynamics: Forces
and Newton’s Laws of Motion
𝐹𝑛𝑒𝑑 = π‘šπ‘Ž
𝑀 = π‘šπ‘”
Chapter 5: Further Applications
of Newton’s Laws: Friction,
Drag, and Elasticity
𝑓𝑠 ≤ πœ‡π‘  𝑁
π‘“π‘˜ = πœ‡π‘˜ 𝑁
1
𝐹𝐷 = πΆπœŒπ΄π‘£ 2
2
𝐹𝑠 = 6πœ‹πœ‚π‘Ÿπ‘£
𝐹 = π‘˜π›₯π‘₯
1𝐹
π›₯𝐿 =
𝐿
π‘Œπ΄ 0
𝐹
π‘ π‘‘π‘Ÿπ‘’π‘ π‘  =
𝐴
π›₯𝐿
π‘ π‘‘π‘Ÿπ‘Žπ‘–π‘› =
𝐿0
π‘ π‘‘π‘Ÿπ‘’π‘ π‘  = π‘Œ × π‘ π‘‘π‘Ÿπ‘Žπ‘–π‘›
1𝐹
π›₯π‘₯ =
𝐿
𝑆𝐴 0
1𝐹
π›₯𝑉 =
𝑉
𝐡𝐴 0
Chapter 6: Uniform Circular
Motion and Gravitation
π›₯𝑠
π‘Ÿ
2πœ‹ π‘Ÿπ‘Žπ‘‘ = 360° = 1 π‘Ÿπ‘’π‘£π‘œπ‘™π‘’π‘‘π‘–π‘œπ‘›
π›₯πœƒ
πœ”=
π›₯𝑑
π›₯πœƒ =
𝑣 = π‘Ÿπœ”
𝑣2
π‘ŽπΆ =
π‘Ÿ
π‘ŽπΆ = π‘Ÿπœ”2
𝐹𝐢 = π‘šπ‘ŽπΆ
π‘šπ‘£ 2
𝐹𝐢 =
π‘Ÿ
𝑣2
π‘‘π‘Žπ‘› πœƒ =
π‘Ÿπ‘”
𝐹𝐢 = π‘šπ‘Ÿπœ”2
π‘šπ‘€
𝐹=𝐺 2
π‘Ÿ
𝐺𝑀
𝑔= 2
π‘Ÿ
𝑇12 π‘Ÿ13
=
𝑇22 π‘Ÿ23
4πœ‹ 2 3
𝑇2 =
π‘Ÿ
𝐺𝑀
π‘Ÿ3
𝐺
=
𝑀
𝑇 2 4πœ‹ 2
Chapter 7: Work, Energy, and
Energy Resources
π‘Š = 𝑓𝑑 π‘π‘œπ‘  πœƒ
1
𝐾𝐸 = π‘šπ‘£ 2
2
1
1
π‘Šπ‘›π‘’π‘‘ = π‘šπ‘£π‘“2 − π‘šπ‘£02
2
2
𝑃𝐸𝑔 = π‘šπ‘”β„Ž
1
𝑃𝐸𝑠 = π‘˜π‘₯ 2
2
𝐾𝐸0 + 𝑃𝐸0 = 𝐾𝐸𝑓 + 𝑃𝐸𝑓
𝐾𝐸0 + 𝑃𝐸0 + π‘Šπ‘›π‘ = 𝐾𝐸𝑓 + 𝑃𝐸𝑓
π‘Šπ‘œπ‘’π‘‘
𝐸𝑓𝑓 =
𝐸𝑖𝑛
π‘Š
𝑃=
𝑑
Chapter 8: Linear Momentum
and Collisions
𝑝 = π‘šπ‘£
π›₯𝑝 = 𝐹𝑛𝑒𝑑 π›₯𝑑
𝑝0 = 𝑝𝑓
π‘š1 𝑣01 + π‘š2 𝑣02 = π‘š1 𝑣𝑓1 + π‘š2 𝑣𝑓2
Please Do Not Write on This Sheet
Thin rod about axis through center
1
1
2
2
π‘š1 𝑣01
+ π‘š2 𝑣02
2
2
1
2
= π‘š1 𝑣𝑓1
2
1
2
+ π‘š2 𝑣𝑓2
2
π‘š1 𝑣1 = π‘š1 𝑣1′ π‘π‘œπ‘  πœƒ1 + π‘š2 𝑣2′ π‘π‘œπ‘  πœƒ2
0 = π‘š1 𝑣1′ 𝑠𝑖𝑛 πœƒ1 + π‘š2 𝑣2′ 𝑠𝑖𝑛 πœƒ2
1
1
1
π‘šπ‘£12 = π‘šπ‘£1′2 + π‘šπ‘£2′2
2
2
2
+ π‘šπ‘£1′ 𝑣2′ π‘π‘œπ‘ (πœƒ1
− πœƒ2 )
𝑣𝑒 π›₯π‘š
π‘Ž=
−𝑔
π‘š π›₯𝑑
𝑣1 π‘š1 + 𝑣2 π‘š2
π‘£π‘π‘š =
π‘š1 + π‘š2
Chapter 9: Statics and Torque
π›₯πœƒ
π›₯𝑑
𝑣 = π‘Ÿπœ”
π›₯πœ”
𝛼=
π›₯𝑑
π›₯𝑣
π‘Žπ‘‘ =
π›₯𝑑
π‘Žπ‘‘ = π‘Ÿπ›Ό
πœƒ = πœ”π‘‘
πœ” = πœ”0 + 𝛼𝑑
1
πœƒ = πœ”0 𝑑 + 𝛼𝑑 2
2
πœ”2 = πœ”02 + 2π›Όπœƒ
πœ”0 + πœ”
πœ”=
2
𝑛𝑒𝑑 𝜏 = 𝐼𝛼
Hoop about cylinder axis: 𝐼 = 𝑀𝑅2
πœ”=
Hoop about any diameter: 𝐼 =
𝑀
2
𝑀𝑅 2
2
(𝑅12 + 𝑅22 )
Solid cylinder (or disk) about
cylinder axis: 𝐼 =
𝑀𝑅 2
2
Solid cylinder (or disk) about
central diameter: 𝐼 =
𝑀𝑅 2
4
+
𝑀ℓ2
12
1
= 𝑃2 + πœŒπ‘£22
2
+ πœŒπ‘”β„Ž2
12
⊥ to length: 𝐼 =
Solid sphere: 𝐼 =
𝑀ℓ2
3
2𝑀𝑅 2
5
Thin spherical shell: 𝐼 =
2𝑀𝑅 2
3
Slab about ⊥ axis through center:
𝐼=
𝑀(π‘Ž2 +𝑏 2 )
12
𝑛𝑒𝑑 π‘Š = (𝑛𝑒𝑑 𝜏)πœƒ
1
πΎπΈπ‘Ÿπ‘œπ‘‘ = πΌπœ”2
2
𝐿 = πΌπœ”
π›₯𝐿
𝑛𝑒𝑑 𝜏 =
π›₯𝑑
π‘š
𝑉
𝐹
𝑃=
𝐴
π‘ƒπ‘Žπ‘‘π‘š = 1.01 × 105 π‘ƒπ‘Ž
𝑃 = πœŒπ‘”β„Ž
𝑃2 = 𝑃1 + πœŒπ‘”β„Ž
𝐹1 𝐹2
=
𝐴1 𝐴2
𝐹𝐡 = 𝑀𝑓𝑙
πœŒπ‘œπ‘π‘—
πΉπ‘Ÿπ‘Žπ‘π‘‘π‘–π‘œπ‘› π‘ π‘’π‘π‘šπ‘’π‘Ÿπ‘”π‘’π‘‘ =
πœŒπ‘“π‘™
𝜌
𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 π‘”π‘Ÿπ‘Žπ‘£π‘–π‘‘π‘¦ =
πœŒπ‘€
𝐹
𝛾=
𝐿
4𝛾
𝑃=
π‘Ÿ
2𝛾 π‘π‘œπ‘  πœƒ
β„Ž=
πœŒπ‘”π‘Ÿ
𝜌=
Chapter 10: Rotational Motion
and Angular Momentum
1
𝑃1 + πœŒπ‘£12 + πœŒπ‘”β„Ž1
2
Thin rod about axis through one end
Chapter 11: Fluid Statics
𝜏 = π‘ŸπΉ 𝑠𝑖𝑛 πœƒ
π‘Ÿ⊥ = π‘Ÿ 𝑠𝑖𝑛 πœƒ
πΉπ‘œ 𝑙𝑖
𝑀𝐴 = =
𝐹𝑖 π‘™π‘œ
𝑙𝑖 𝐹𝑖 = π‘™π‘œ πΉπ‘œ
Ring: 𝐼 =
⊥ to length: 𝐼 =
𝑀ℓ2
Chapter 12: Fluid Dynamics
and Its Biological Medical
Applications
𝑉
𝑄=
𝑑
𝑄 = 𝐴𝑣
𝐴1 𝑣1 = 𝐴2 𝑣2
𝑛1 𝐴1 𝑣1 = 𝑛2 𝐴2 𝑣2
1
(Δ𝑃 + Δ πœŒπ‘£ 2 + ΔπœŒπ‘”β„Ž) 𝑄 = π‘π‘œπ‘€π‘’π‘Ÿ
2
𝑣1 = √2π‘”β„Ž
𝐹𝐿
πœ‚=
𝑣𝐴
𝑃2 − 𝑃1
𝑄=
𝑅
8πœ‚π‘™
𝑅= 4
πœ‹π‘Ÿ
(𝑃2 − 𝑃1 )πœ‹π‘Ÿ 4
𝑄=
8πœ‚π‘™
2πœŒπ‘£π‘Ÿ
𝑁𝑅 =
πœ‚
πœŒπ‘£πΏ
𝑁𝑅′ =
πœ‚
π‘₯π‘Ÿπ‘šπ‘  = √2𝐷𝑑
Chapter 13: Temperature,
Kinetic Theory, and the Gas
Laws
9
𝑇(°πΆ) + 32
5
𝑇(𝐾) = 𝑇(°πΆ) + 273.15
π›₯𝐿 = 𝛼𝐿π›₯𝑇
π›₯𝐴 = 2𝛼𝐴π›₯𝑇
π›₯𝑉 = 𝛽𝑉π›₯𝑇
𝛽 ≈ 3𝛼
𝑃𝑉 = π‘π‘˜π‘‡
π‘˜ = 1.38 × 10−23 𝐽/𝐾
𝑁𝐴 = 6.02 × 1023 π‘šπ‘œπ‘™ −1
𝑃𝑉 = 𝑛𝑅𝑇
𝐽
𝑅 = 8.31
π‘šπ‘œπ‘™ ⋅ 𝐾
1
2
𝑃𝑉 = π‘π‘šπ‘£
3
1
3
2
𝐾𝐸 = π‘šπ‘£ = π‘˜π‘‡
2
2
𝑇(°πΉ) =
π‘£π‘Ÿπ‘šπ‘  = √
3π‘˜π‘‡
π‘š
% π‘Ÿπ‘’π‘™π‘Žπ‘‘π‘–π‘£π‘’ β„Žπ‘’π‘šπ‘–π‘‘π‘–π‘‘π‘¦
π‘£π‘Žπ‘π‘œπ‘Ÿ 𝑑𝑒𝑛𝑠𝑖𝑑𝑦
=
π‘ π‘Žπ‘‘π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› π‘£π‘Žπ‘π‘œπ‘Ÿ π‘‘π‘’π‘›π‘Žπ‘ π‘–π‘‘π‘¦
× 100%
Chapter 14: Heat and Heat
Transfer Methods
1.000 π‘˜π‘π‘Žπ‘™ = 4186 𝐽
𝑄 = π‘šπ‘π›₯𝑇
𝑄 = π‘šπΏπ‘“
𝑄 = π‘šπΏπ‘£
𝑄 π‘˜π΄(𝑇2 − 𝑇1 )
=
𝑑
𝑑
𝑄
= πœŽπ‘’π΄π‘‡ 4
𝑑
𝐽
𝜎 = 5.67 × 10−8
𝑠 ⋅ π‘š2 ⋅ 𝐾 4
𝑄𝑛𝑒𝑑
= πœŽπ‘’π΄(𝑇24 − 𝑇14 )
𝑑
Chapter 15: Thermodynamics
3
π‘ˆ = π‘π‘˜π‘‡
2
π›₯π‘ˆ = 𝑄 − π‘Š
π‘Š = 𝑃π›₯𝑉 (π‘–π‘ π‘œπ‘π‘Žπ‘Ÿπ‘–π‘ π‘π‘Ÿπ‘œπ‘π‘’π‘ π‘ )
Δπ‘ˆ = 𝑄 − 𝑃Δ𝑉
π‘Š = 0 (π‘–π‘ π‘œπ‘β„Žπ‘œπ‘Ÿπ‘–π‘ π‘π‘Ÿπ‘œπ‘π‘’π‘ π‘ )
Δπ‘ˆ = 𝑄
𝑄 = π‘Š (π‘–π‘ π‘œπ‘‘β„Žπ‘’π‘Ÿπ‘šπ‘Žπ‘™ π‘π‘Ÿπ‘œπ‘π‘’π‘ π‘ )
Δπ‘ˆ = 0
𝑄 = 0 (π‘Žπ‘‘π‘–π‘Žπ‘π‘Žπ‘‘π‘–π‘ π‘π‘Ÿπ‘œπ‘π‘’π‘ π‘ )
Δπ‘ˆ = −π‘Š
π‘Š
𝐸𝑓𝑓 =
π‘„β„Ž
𝑄𝑐
(π‘π‘¦π‘π‘™π‘–π‘π‘Žπ‘™ π‘π‘Ÿπ‘œπ‘π‘’π‘ π‘ )
𝐸𝑓𝑓 = 1 −
π‘„β„Ž
𝑇𝑐
𝐸𝑓𝑓𝐢 = 1 −
π‘‡β„Ž
π‘„β„Ž
πΆπ‘‚π‘ƒβ„Žπ‘ =
π‘Š
𝑄𝑐
πΆπ‘‚π‘ƒπ‘Ÿπ‘’π‘“ = πΆπ‘‚π‘ƒβ„Žπ‘ − 1 =
π‘Š
𝑄𝑐 ⁄𝑑1
𝐸𝐸𝑅 =
π‘„β„Ž ⁄𝑑2
𝑄
π›₯𝑆 =
𝑇
π‘„β„Ž 𝑄𝑐
π›₯π‘†π‘‘π‘œπ‘‘ =
+
=0
π‘‡β„Ž 𝑇𝑐
π‘Šπ‘’π‘›π‘Žπ‘£π‘Žπ‘–π‘™ = π›₯𝑆 ⋅ 𝑇0
𝑆 = π‘˜ 𝑙𝑛 π‘Š
π‘˜ = 1.38 × 10−23 𝐽/𝐾
Chapter 16: Oscillatory Motion
and Waves
1
𝑓=
𝑇
πœ†
𝑣 = = π‘“πœ†
𝑇
𝐹 = −π‘˜π‘₯
Please Do Not Write on This Sheet
1
𝑃𝐸𝑒𝑙 = π‘˜π‘₯ 2
2
π‘š
𝑇 = 2πœ‹√
π‘˜
𝑓=
1 π‘˜
√
2πœ‹ π‘š
2πœ‹π‘‘
π‘₯(𝑑) = 𝑋 π‘π‘œπ‘  (
)
𝑇
2πœ‹π‘‘
𝑣(𝑑) = −π‘£π‘šπ‘Žπ‘₯ 𝑠𝑖𝑛 (
)
𝑇
π‘£π‘šπ‘Žπ‘₯ =
2πœ‹π‘‹
π‘˜
= 𝑋√
𝑇
π‘š
π‘Ž(𝑑) = −
π‘˜π‘‹
2πœ‹π‘‘
π‘π‘œπ‘  (
)
π‘š
𝑇
𝐹
π‘£π‘ π‘‘π‘Ÿπ‘–π‘›π‘” = √
π‘š/𝐿
𝑣𝑀 = (331
π‘š
𝑇
)√
𝑠
273 𝐾
𝑃
𝐼=
𝐴
π΄π‘ π‘β„Žπ‘’π‘Ÿπ‘’ = 4πœ‹π‘Ÿ 2
(π›₯𝑝)2
𝐼=
2πœŒπ‘£π‘€
Chapter 17: Physics of Hearing
𝐼
𝛽 = (10 𝑑𝐡) π‘™π‘œπ‘” ( )
𝐼0
𝑣𝑀 ± π‘£π‘œ
π‘“π‘œ = 𝑓𝑠 (
)
𝑣𝑀 βˆ“ 𝑣𝑠
𝑓𝐡 = |𝑓1 − 𝑓2 |
𝑣𝑀
𝑓𝑛 = 𝑛 ( )
2𝐿
𝑣𝑀
𝑓𝑛 = 𝑛 ( )
4𝐿
𝑍 = πœŒπ‘£
(𝑍2 − 𝑍1 )2
π‘Ž=
(𝑍1 + 𝑍2 )2
Chapter 18: Electric Charge
and Electric Field
|π‘žπ‘’ | = 1.60 × 10−19 𝐢
|π‘ž1 π‘ž2 |
𝐹=π‘˜
π‘Ÿ2
𝐸 = 𝐹/π‘ž
|𝑄|
𝐸=π‘˜ 2
π‘Ÿ
Chapter 19: Electric Potential
and Electric Energy
𝑃𝐸
π‘ž
π›₯𝑃𝐸 = π‘žπ›₯𝑉
π‘Š = π‘žπ‘‰π΄π΅
𝑉𝐴𝐡
𝐸=
𝑑
π›₯𝑉
𝐸=−
π›₯𝑠
π‘˜π‘„
𝑉=
π‘Ÿ
𝑄
𝐢=
𝑉
𝐴
𝐢 = πœ–0
𝑑
𝑉=
πœ–0 = 8.85 × 10−12
𝐹
π‘š
𝐴
𝑑
𝑄𝑉 𝐢𝑉 2 𝑄2
πΈπ‘π‘Žπ‘ =
=
=
2
2
2𝐢
𝐢 = πœ…πœ–0
Chapter 20: Electric Current,
Resistance, and Ohm’s Law
π›₯𝑄
π›₯𝑑
𝐼 = π‘›π‘žπ΄π‘£π‘‘
𝑉 = 𝐼𝑅
𝜌𝐿
𝑅=
𝐴
𝜌 = 𝜌0 (1 + 𝛼π›₯𝑇)
𝑅 = 𝑅0 (1 + 𝛼π›₯𝑇)
𝑉2
𝑃 = 𝐼𝑉 =
= 𝐼2 𝑅
𝑅
1
π‘ƒπ‘Žπ‘£π‘’ = 𝐼0 𝑉0
2
𝐼0
πΌπ‘Ÿπ‘šπ‘  =
√2
𝑉0
π‘‰π‘Ÿπ‘šπ‘  =
√2
𝐼=
Chapter 21: Circuits,
Bioelectricity, and DC
Instruments
𝑅𝑆 = 𝑅1 + 𝑅2 + 𝑅3 + β‹―
1
1
1
1
=
+
+
+β‹―
𝑅𝑃 𝑅1 𝑅2 𝑅3
𝑉 = π‘’π‘šπ‘“ − πΌπ‘Ÿ
𝑑
𝑉 = π‘’π‘šπ‘“ (1 − 𝑒 −𝑅𝐢 )
𝜏 = 𝑅𝐢
𝑑
𝑉 = 𝑉0 𝑒 −π‘ŸπΆ
Chapter 22: Magnetism
𝐹 = π‘žπ‘£π΅ 𝑠𝑖𝑛 πœƒ
π‘šπ‘£
π‘Ÿ=
π‘žπ΅
πœ– = 𝐡𝑙𝑣
𝐹 = 𝐼𝐿𝐡 𝑠𝑖𝑛 πœƒ
𝜏 = 𝑁𝐼𝐴𝐡 𝑠𝑖𝑛 πœƒ
πœ‡0 𝐼
𝐡=
2πœ‹π‘Ÿ
πœ‡0 𝐼
𝐡=
2𝑅
𝐡 = πœ‡0 𝑛𝐼
𝐹 πœ‡0 𝐼1 𝐼2
=
𝑙
2πœ‹π‘Ÿ
Chapter 23: Electromagnetic
Induction, AC Circuits, and
Electrical Technologies
𝛷 = 𝐡𝐴 π‘π‘œπ‘  πœƒ
π›₯𝛷
π‘’π‘šπ‘“ = −𝑁
π›₯𝑑
π‘’π‘šπ‘“ = 𝑣𝐡𝐿
π‘’π‘šπ‘“ = π‘π΄π΅πœ” 𝑠𝑖𝑛 πœ”π‘‘
𝑉𝑆 𝑁𝑆 𝐼𝑃
=
=
𝑉𝑃 𝑁𝑃 𝐼𝑆
π›₯𝐼2
π‘’π‘šπ‘“1 = −𝑀
π›₯𝑑
π›₯𝐼
π‘’π‘šπ‘“ = −𝐿
π›₯𝑑
π›₯𝛷
𝐿=𝑁
π›₯𝐼
μ0 𝑁 2 𝐴
𝐿=
β„“
1 2
𝐸𝑖𝑛𝑑 = 𝐿𝐼
2
𝑑
𝐼 = 𝐼0 (1 − 𝑒 −𝜏 )
𝜏=
𝐿
𝑅
Please Do Not Write on This Sheet
𝑅
π‘π‘œπ‘  πœ™ =
𝑍
π‘ƒπ‘Žπ‘£π‘’ = πΌπ‘Ÿπ‘šπ‘  π‘‰π‘Ÿπ‘šπ‘  π‘π‘œπ‘  πœ™
Chapter 24: Electromagnetic
Waves
𝑐=
1
√πœ‡ 0 πœ–0
𝐸
=𝑐
𝐡
𝑐 = π‘“πœ†
π‘πœ–0 𝐸02
πΌπ‘Žπ‘£π‘’ =
2
𝑐𝐡02
πΌπ‘Žπ‘£π‘’ =
2πœ‡0
𝐸0 𝐡0
πΌπ‘Žπ‘π‘’ =
2πœ‡0
Chapter 25: Geometric Optics
πœƒπ‘– = πœƒπ‘Ÿ
𝑐
𝑛=
𝑣
𝑛1 𝑠𝑖𝑛 πœƒ1 = 𝑛2 𝑠𝑖𝑛 πœƒ2
𝑛2
πœƒπ‘ = 𝑠𝑖𝑛−1
𝑛1
1
𝑃=
𝑓
1
1
1
=
+
𝑓 π‘‘π‘œ 𝑑𝑖
β„Žπ‘–
𝑑𝑖
π‘š=
=−
β„Žπ‘œ
π‘‘π‘œ
𝑅
𝑓=
2
𝑑
Chapter 28: Special Relativity
π›₯𝑑 =
𝛾=
Chapter 27: Wave Optics
πœ†π‘› =
πœ†
𝑛
sin πœƒ = π‘š
πœ†
𝑑
2
√1 − 𝑣2
𝑐
1
2
√1 − 𝑣2
𝑐
𝑣2
𝑐2
𝑣𝐿𝑇 + 𝑣𝑇𝐺
𝑣𝐿𝐺 =
𝑣 𝑣
1 + 𝐿𝑇 2 𝑇𝐺
𝑐
𝑒
1+
𝑐
πœ†π‘œπ‘π‘  = πœ†π‘  √
𝑒
1−
𝑐
𝑒
𝑐
𝑒
1+
𝑐
π‘šπ‘£
π‘“π‘œπ‘π‘  = 𝑓𝑠 √
𝑝=
1
1
+
π‘‘π‘œ 𝑑𝑖
π‘š = π‘šπ‘œ π‘šπ‘’
𝑁𝐴 = 𝑛 𝑠𝑖𝑛 𝛼
𝑓
1
𝑓/# = ≈
𝐷 2𝑁𝐴
𝑑𝑖 = π‘“π‘œ
π‘“π‘œ
𝑀=
𝑓𝑒
π›₯𝑑0
𝐿 = 𝐿0 √1 −
Chapter 26: Vision and Optical
Instruments
𝑃=
𝐼 = 𝐼0 𝑒 −𝜏
𝑉
𝐼=
𝑋𝐿
𝑋𝐿 = 2πœ‹π‘“πΏ
𝑉
𝐼=
𝑋𝐢
1
𝑋𝐢 =
2πœ‹π‘“πΆ
𝑉0
π‘‰π‘Ÿπ‘šπ‘ 
𝐼0 =
π‘œπ‘Ÿ πΌπ‘Ÿπ‘šπ‘  =
𝑍
𝑍
𝑍 = √𝑅2 + (𝑋𝐿 − 𝑋𝐢 )2
1
𝑓0 =
2πœ‹√𝐿𝐢
1 πœ†
𝑠𝑖𝑛 πœƒ = (π‘š + )
2 𝑑
πœ†
𝑠𝑖𝑛 πœƒ = π‘š
π‘Š
πœ†
πœƒ = 1.22
𝐷
πœ†π‘›
2𝑑 =
2
2𝑑 = πœ†π‘›
I = ½ I0
𝐼 = 𝐼0 π‘π‘œπ‘  2 πœƒ
𝑛2
π‘‘π‘Žπ‘› πœƒπ‘ =
𝑛1
𝐸=
1−
2
√1 − 𝑣2
𝑐
2
π‘šπ‘
2
√1 − 𝑣2
𝑐
𝐸0 = π‘šπ‘ 2
π‘šπ‘ 2
πΎπΈπ‘Ÿπ‘’π‘™ =
− π‘šπ‘ 2
2
√1 − 𝑣2
𝑐
2
2
𝐸 = (𝑝𝑐) + (π‘šπ‘ 2 )2
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