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Chapter 1: Introduction: The

Nature of Science and Physics

𝑥 =

−𝑏 ± √𝑏

2

− 4 𝑎𝑐

2 𝑎

𝑅𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝐸𝑎𝑟𝑡ℎ = 6. 38 × 10

6

𝑚

𝑀𝑎𝑠𝑠 𝑜𝑓 𝐸𝑎𝑟𝑡ℎ = 5. 98 × 10

24

𝑘𝑔

𝑐 = 3. 00 × 10

8

𝑚/𝑠

𝐺 = 6. 673 × 10

− 11

𝑁𝑚

2

𝑘𝑔

2

𝑁

𝐴

= 6. 02 × 10

23

𝑘 = 1. 38 × 10

− 23

𝐽/𝐾

𝑅 = 8. 31

𝐽

𝑚𝑜𝑙 ⋅ 𝐾

⁄

𝜎 = 5. 67 × 10

− 8

𝑊/(𝑚

2

⋅ 𝐾)

𝑘 = 8. 99 × 10

9

𝑁 ⋅ 𝑚

2

/𝐶

2

𝑞

𝑒

= − 1. 60 × 10

− 19

𝐶

𝜖

0

= 8. 85 × 10

− 12

𝐶

2

/(𝑁 ⋅ 𝑚

2

)

𝜇

0

= 4π × 10

− 7

𝑇 ⋅ 𝑚/𝐴

ℎ = 6. 63 × 10

− 34

𝐽 ⋅ 𝑠

𝑚

𝑒

= 9. 11 × 10

− 31

𝑘𝑔

𝑚

𝑝

= 1. 6726 × 10

− 27

𝑘𝑔

𝑚

𝑛

= 1. 6749 × 10

− 27

𝑘𝑔

𝑎𝑚𝑢 = 1. 6605 × 10

− 27

𝑘𝑔

𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 = 1000

𝑘𝑔

𝑚

3

Chapter 2: Kinematics

𝛥𝑥 = 𝑥

𝑓

− 𝑥

0

𝛥𝑡 = 𝑡

𝑓

− 𝑡

0

𝑣 =

𝛥𝑥

𝛥𝑡

=

𝑥

𝑓

− 𝑥

0

𝑡

𝑓

− 𝑡

0

𝑎 =

𝛥𝑣

𝛥𝑡

=

𝑣

𝑓

− 𝑣

0

𝑡

𝑓

− 𝑡

0

𝑥 = 𝑥

0

+ 𝑣𝑡

𝑣 =

𝑣

0

+ 𝑣

𝑣 = 𝑣

0

+ 𝑎𝑡

𝑥 = 𝑥

0

+ 𝑣

0

𝑡 +

𝑎𝑡

2

𝑣

2

= 𝑣

0

2

+ 2 𝑎(𝑥 − 𝑥

0

)

𝑔 = 9. 80

𝑚

𝑠

2

Chapter 3: Two-Dimensional

Kinematics

𝐴

𝑥

= 𝐴 𝑐𝑜𝑠 𝜃

𝐴

𝑦

= 𝐴 𝑠𝑖𝑛 𝜃

𝑅

𝑥

= 𝐴

𝑥

+ 𝐵

𝑥

𝑅

𝑦

= 𝐴

𝑦

+ 𝐵

𝑦

𝑅 = √𝑅

𝑥

2

+ 𝑅

𝑦

2

𝜃 = 𝑡𝑎𝑛

− 1

𝑅

𝑦

𝑅

𝑥

ℎ =

𝑣

0 𝑦

2

2 𝑔

𝑅 =

𝑣

0

2

𝑠𝑖𝑛 2 𝜃

0

𝑔

𝑣

𝑥

= 𝑣 𝑐𝑜𝑠 𝜃

𝑣

𝑦

= 𝑣 𝑠𝑖𝑛 𝜃

𝑣 =

√

𝑣

𝑥

2

+ 𝑣

𝑦

2

𝜃 = 𝑡𝑎𝑛

− 1

𝑣

𝑦

𝑣

𝑥

Chapter 4: Dynamics: Forces

and Newton’s Laws of Motion

𝐹

𝑛𝑒𝑡

= 𝑚𝑎

𝑤 = 𝑚𝑔

Chapter 5: Further Applications

of Newton’s Laws: Friction,

Drag, and Elasticity

𝑓

𝑠

≤ 𝜇

𝑠

𝑁

𝑓

𝑘

= 𝜇

𝑘

𝑁

𝐹

𝐷

=

𝐶𝜌𝐴𝑣

2

𝐹

𝑠

= 6 𝜋𝜂𝑟𝑣

𝐹 = 𝑘𝛥𝑥

𝛥𝐿 =

1 𝐹

𝑌𝐴

𝐿

0

𝑠𝑡𝑟𝑒𝑠𝑠 =

𝐹

𝐴

𝑠𝑡𝑟𝑎𝑖𝑛 =

𝛥𝐿

𝐿

0

𝑠𝑡𝑟𝑒𝑠𝑠 = 𝑌 × 𝑠𝑡𝑟𝑎𝑖𝑛

𝛥𝑥 =

1 𝐹

𝑆𝐴

𝐿

0

𝛥𝑉 =

1 𝐹

𝐵𝐴

𝑉

0

Chapter 6: Uniform Circular

Motion and Gravitation

𝛥𝜃 =

𝛥𝑠

𝑟

2 𝜋 𝑟𝑎𝑑 = 360° = 1 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛

𝜔 =

𝛥𝜃

𝛥𝑡

𝑣 = 𝑟𝜔

𝑎

𝐶

=

𝑣

2

𝑟

𝑎

𝐶

= 𝑟𝜔

2

𝐹

𝐶

= 𝑚𝑎

𝐶

𝐹

𝐶

=

𝑚𝑣

2

𝑟

𝑡𝑎𝑛 𝜃 =

𝑣

2

𝑟𝑔

𝐹

𝐶

= 𝑚𝑟𝜔

2

𝐹 = 𝐺

𝑚𝑀

𝑟

2

𝑔 =

𝐺𝑀

𝑟

2

𝑇

1

2

𝑇

2

2

=

𝑟

1

3

𝑟

2

3

𝑇

2

=

4 𝜋

2

𝐺𝑀

𝑟

3

𝑟

3

𝑇

2

=

𝐺

4 𝜋

2

𝑀

Chapter 7: Work, Energy, and

Energy Resources

𝑊 = 𝑓𝑑 𝑐𝑜𝑠 𝜃

𝐾𝐸 =

𝑚𝑣

2

𝑊

𝑛𝑒𝑡

=

𝑚𝑣

𝑓

2

−

𝑚𝑣

0

2

𝑃𝐸

𝑔

= 𝑚𝑔ℎ

𝑃𝐸

𝑠

=

𝑘𝑥

2

𝐾𝐸

0

+ 𝑃𝐸

0

= 𝐾𝐸

𝑓

+ 𝑃𝐸

𝑓

𝐾𝐸

0

+ 𝑃𝐸

0

+ 𝑊

𝑛𝑐

= 𝐾𝐸

𝑓

+ 𝑃𝐸

𝑓

𝐸𝑓𝑓 =

𝑊

𝑜𝑢𝑡

𝐸

𝑖𝑛

𝑃 =

𝑊

𝑡

Chapter 8: Linear Momentum

and Collisions

𝑝 = 𝑚𝑣

𝛥𝑝 = 𝐹

𝑛𝑒𝑡

𝛥𝑡

𝑝

0

= 𝑝

𝑓

𝑚

1

𝑣

01

+ 𝑚

2

𝑣

02

= 𝑚

1

𝑣

𝑓 1

+ 𝑚

2

𝑣

𝑓 2

𝑚

1

𝑣

01

2

+

𝑚

2

𝑣

02

2

=

𝑚

1

𝑣

𝑓 1

2

+

𝑚

2

𝑣

𝑓 2

2

𝑚

1

𝑣

1

= 𝑚

1

𝑣

1

′

𝑐𝑜𝑠 𝜃

1

+ 𝑚

2

𝑣

2

′

𝑐𝑜𝑠 𝜃

2

0 = 𝑚

1

𝑣

1

′

𝑠𝑖𝑛 𝜃

1

+ 𝑚

2

𝑣

2

′

𝑠𝑖𝑛 𝜃

2

𝑚𝑣

1

2

=

𝑚𝑣

1

′

+

𝑚𝑣

2

′

+ 𝑚𝑣

1

′

𝑣

2

′

𝑐𝑜𝑠(𝜃

1

− 𝜃

2

)

𝑎 =

𝑣

𝑒

𝑚

𝛥𝑚

𝛥𝑡

− 𝑔

𝑣

𝑐𝑚

=

𝑣

1

𝑚

1

+ 𝑣

2

𝑚

2

𝑚

1

+ 𝑚

2

Chapter 9: Statics and Torque

𝜏 = 𝑟𝐹 𝑠𝑖𝑛 𝜃

𝑟

⊥

= 𝑟 𝑠𝑖𝑛 𝜃

𝑀𝐴 =

𝐹

𝑜

𝐹

𝑖

=

𝑙

𝑖

𝑙

𝑜

𝑙

𝑖

𝐹

𝑖

= 𝑙

𝑜

𝐹

𝑜

Chapter 10: Rotational Motion

and Angular Momentum

𝜔 =

𝛥𝜃

𝛥𝑡

𝑣 = 𝑟𝜔

𝛼 =

𝛥𝜔

𝛥𝑡

𝑎

𝑡

=

𝛥𝑣

𝛥𝑡

𝑎

𝑡

= 𝑟𝛼

𝜃 = 𝜔𝑡

𝜔 = 𝜔

0

+ 𝛼𝑡

𝜃 = 𝜔

0

𝑡 +

𝛼𝑡

2

𝜔

2

= 𝜔

0

2

+ 2 𝛼𝜃

𝜔 =

𝜔

0

+ 𝜔

𝑛𝑒𝑡 𝜏 = 𝐼𝛼

Hoop about cylinder axis: 𝐼 = 𝑀𝑅

2

Hoop about any diameter: 𝐼 =

𝑀𝑅

2

2

Ring: 𝐼 =

𝑀

2

(

𝑅

1

2

+ 𝑅

2

2

)

Solid cylinder (or disk) about

cylinder axis: 𝐼 =

𝑀𝑅

2

2

Solid cylinder (or disk) about

central diameter: 𝐼 =

𝑀𝑅

2

4

+

𝑀ℓ

2

12

Thin rod about axis through center

⊥ to length: 𝐼 =

𝑀ℓ

2

12

Thin rod about axis through one end

⊥ to length: 𝐼 =

𝑀ℓ

2

3

Solid sphere: 𝐼 =

2 𝑀𝑅

2

5

Thin spherical shell: 𝐼 =

2 𝑀𝑅

2

3

Slab about ⊥ axis through center:

𝐼 =

𝑀(𝑎

2

+𝑏

2

)

12

𝑛𝑒𝑡 𝑊 = (𝑛𝑒𝑡 𝜏)𝜃

𝐾𝐸

𝑟𝑜𝑡

=

𝐼𝜔

2

𝐿 = 𝐼𝜔

𝑛𝑒𝑡 𝜏 =

𝛥𝐿

𝛥𝑡

Chapter 11: Fluid Statics

𝜌 =

𝑚

𝑉

𝑃 =

𝐹

𝐴

𝑃

𝑎𝑡𝑚

= 1. 01 × 10

5

𝑃𝑎

𝑃 = 𝜌𝑔ℎ

𝑃

2

= 𝑃

1

+ 𝜌𝑔ℎ

𝐹

1

𝐴

1

=

𝐹

2

𝐴

2

𝐹

𝐵

= 𝑤

𝑓𝑙

𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑠𝑢𝑏𝑚𝑒𝑟𝑔𝑒𝑑 =

𝜌

𝑜𝑏𝑗

𝜌

𝑓𝑙

𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 =

𝜌

𝜌

𝑤

𝛾 =

𝐹

𝐿

𝑃 =

4 𝛾

𝑟

ℎ =

2 𝛾 𝑐𝑜𝑠 𝜃

𝜌𝑔𝑟

Chapter 12: Fluid Dynamics

and Its Biological Medical

Applications

𝑄 =

𝑉

𝑡

𝑄 = 𝐴𝑣

𝐴

1

𝑣

1

= 𝐴

2

𝑣

2

𝑛

1

𝐴

1

𝑣

1

= 𝑛

2

𝐴

2

𝑣

2

𝑃

1

+

𝜌𝑣

1

2

+ 𝜌𝑔ℎ

1

= 𝑃

2

+

𝜌𝑣

2

2

+ 𝜌𝑔ℎ

2

(Δ𝑃 + Δ

𝜌𝑣

2

+ Δ𝜌𝑔ℎ) 𝑄 = 𝑝𝑜𝑤𝑒𝑟

𝑣

1

= √ 2 𝑔ℎ

𝜂 =

𝐹𝐿

𝑣𝐴

𝑄 =

𝑃

2

− 𝑃

1

𝑅

𝑅 =

8 𝜂𝑙

𝜋𝑟

4

𝑄 =

(𝑃

2

− 𝑃

1

)𝜋𝑟

4

8 𝜂𝑙

𝑁

𝑅

=

2 𝜌𝑣𝑟

𝜂

𝑁

𝑅

′

=

𝜌𝑣𝐿

𝜂

𝑥

𝑟𝑚𝑠

= √ 2 𝐷𝑡

Chapter 13: Temperature,

Kinetic Theory, and the Gas

Laws

𝑇

(

°𝐹

)

=

𝑇

(

°𝐶

)

𝑇(𝐾) = 𝑇(°𝐶) + 273. 15

𝛥𝐿 = 𝛼𝐿𝛥𝑇

𝛥𝐴 = 2 𝛼𝐴𝛥𝑇

𝛥𝑉 = 𝛽𝑉𝛥𝑇

𝛽 ≈ 3 𝛼

𝑃𝑉 = 𝑁𝑘𝑇

𝑘 = 1. 38 × 10

− 23

𝐽/𝐾

𝑁

𝐴

= 6. 02 × 10

23

𝑚𝑜𝑙

− 1

𝑃𝑉 = 𝑛𝑅𝑇

𝑅 = 8. 31

𝐽

𝑚𝑜𝑙 ⋅ 𝐾

𝑃𝑉 =

𝑁𝑚𝑣

2

𝐾𝐸 =

𝑚𝑣

2

=

𝑘𝑇

𝑣

𝑟𝑚𝑠

=

√

3 𝑘𝑇

𝑚

% 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 ℎ𝑢𝑚𝑖𝑑𝑖𝑡𝑦

=

𝑣𝑎𝑝𝑜𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦

𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑣𝑎𝑝𝑜𝑟 𝑑𝑒𝑛𝑎𝑠𝑖𝑡𝑦

× 100%

Chapter 14: Heat and Heat

Transfer Methods

1. 000 𝑘𝑐𝑎𝑙 = 4186 𝐽

𝑄 = 𝑚𝑐𝛥𝑇

𝑄 = 𝑚𝐿

𝑓

𝑄 = 𝑚𝐿

𝑣

𝑄

𝑡

=

𝑘𝐴(𝑇

2

− 𝑇

1

)

𝑑

𝑄

𝑡

= 𝜎𝑒𝐴𝑇

4

𝜎 = 5. 67 × 10

− 8

𝐽

𝑠 ⋅ 𝑚

2

⋅ 𝐾

4

𝑄

𝑛𝑒𝑡

𝑡

= 𝜎𝑒𝐴(𝑇

2

4

− 𝑇

1

4

)

Chapter 15: Thermodynamics

𝑈 =

𝑁𝑘𝑇

𝛥𝑈 = 𝑄 − 𝑊

𝑊 = 𝑃𝛥𝑉 (𝑖𝑠𝑜𝑏𝑎𝑟𝑖𝑐 𝑝𝑟𝑜𝑐𝑒𝑠𝑠)

Δ𝑈 = 𝑄 − 𝑃Δ𝑉

𝑊 = 0 (𝑖𝑠𝑜𝑐ℎ𝑜𝑟𝑖𝑐 𝑝𝑟𝑜𝑐𝑒𝑠𝑠)

Δ𝑈 = 𝑄

𝑄 = 𝑊 (𝑖𝑠𝑜𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑝𝑟𝑜𝑐𝑒𝑠𝑠)

Δ𝑈 = 0

𝑄 = 0

(

𝑎𝑑𝑖𝑎𝑏𝑎𝑡𝑖𝑐 𝑝𝑟𝑜𝑐𝑒𝑠𝑠

)

Δ𝑈 = −𝑊

𝐸𝑓𝑓 =

𝑊

𝑄

ℎ

𝐸𝑓𝑓 = 1 −

𝑄

𝑐

𝑄

ℎ

(

𝑐𝑦𝑐𝑙𝑖𝑐𝑎𝑙 𝑝𝑟𝑜𝑐𝑒𝑠𝑠

)

𝐸𝑓𝑓

𝐶

= 1 −

𝑇

𝑐

𝑇

ℎ

𝐶𝑂𝑃

ℎ𝑝

=

𝑄

ℎ

𝑊

𝐶𝑂𝑃

𝑟𝑒𝑓

= 𝐶𝑂𝑃

ℎ𝑝

− 1 =

𝑄

𝑐

𝑊

𝐸𝐸𝑅 =

𝑄

𝑐

𝑡

1

⁄

𝑄

ℎ

𝑡

2

⁄

𝛥𝑆 =

𝑄

𝑇

𝛥𝑆

𝑡𝑜𝑡

=

𝑄

ℎ

𝑇

ℎ

+

𝑄

𝑐

𝑇

𝑐

= 0

𝑊

𝑢𝑛𝑎𝑣𝑎𝑖𝑙

= 𝛥𝑆 ⋅ 𝑇

0

𝑆 = 𝑘 𝑙𝑛 𝑊

𝑘 = 1. 38 × 10

− 23

𝐽/𝐾

Chapter 16: Oscillatory Motion

and Waves

𝑓 =

𝑇

𝑣 =

𝜆

𝑇

= 𝑓𝜆

𝐹 = −𝑘𝑥

𝑃𝐸

𝑒𝑙

=

𝑘𝑥

2

𝑇 = 2 𝜋√

𝑚

𝑘

𝑓 =

2 𝜋

√

𝑘

𝑚

𝑥

(

𝑡

)

= 𝑋 𝑐𝑜𝑠 (

2 𝜋𝑡

𝑇

)

𝑣(𝑡) = −𝑣

𝑚𝑎𝑥

𝑠𝑖𝑛 (

2 𝜋𝑡

𝑇

)

𝑣

𝑚𝑎𝑥

=

2 𝜋𝑋

𝑇

= 𝑋

√

𝑘

𝑚

𝑎(𝑡) = −

𝑘𝑋

𝑚

𝑐𝑜𝑠 (

2 𝜋𝑡

𝑇

)

𝑣

𝑠𝑡𝑟𝑖𝑛𝑔

= √

𝐹

𝑚/𝐿

𝑣

𝑤

= ( 331

𝑚

𝑠

)

√

𝑇

273 𝐾

𝐼 =

𝑃

𝐴

𝐴

𝑠𝑝ℎ𝑒𝑟𝑒

= 4 𝜋𝑟

2

𝐼 =

(

𝛥𝑝

)

2

2 𝜌𝑣

𝑤

Chapter 17: Physics of Hearing

𝛽 =

(

10 𝑑𝐵

)

𝑙𝑜𝑔 (

𝐼

𝐼

0

)

𝑓

𝑜

= 𝑓

𝑠

(

𝑣

𝑤

± 𝑣

𝑜

𝑣

𝑤

∓ 𝑣

𝑠

)

𝑓

𝐵

= |𝑓

1

− 𝑓

2

|

𝑓

𝑛

= 𝑛 (

𝑣

𝑤

2 𝐿

)

𝑓

𝑛

= 𝑛 (

𝑣

𝑤

4 𝐿

)

𝑍 = 𝜌𝑣

𝑎 =

(

𝑍

2

− 𝑍

1

)

2

(𝑍

1

+ 𝑍

2

)

2

Chapter 18: Electric Charge

and Electric Field

|𝑞

𝑒

| = 1. 60 × 10

− 19

𝐶

𝐹 = 𝑘

|𝑞

1

𝑞

2

|

𝑟

2

𝐸 = 𝐹/𝑞

𝐸 = 𝑘

|

𝑄

|

𝑟

2

Chapter 19: Electric Potential

and Electric Energy

𝑉 =

𝑃𝐸

𝑞

𝛥𝑃𝐸 = 𝑞𝛥𝑉

𝑊 = 𝑞𝑉

𝐴𝐵

𝐸 =

𝑉

𝐴𝐵

𝑑

𝐸 = −

𝛥𝑉

𝛥𝑠

𝑉 =

𝑘𝑄

𝑟

𝐶 =

𝑄

𝑉

𝐶 = 𝜖

0

𝐴

𝑑

𝜖

0

= 8. 85 × 10

− 12

𝐹

𝑚

𝐶 = 𝜅𝜖

0

𝐴

𝑑

𝐸

𝑐𝑎𝑝

=

𝑄𝑉

=

𝐶𝑉

2

=

𝑄

2

2 𝐶

Chapter 20: Electric Current,

Resistance, and Ohm’s Law

𝐼 =

𝛥𝑄

𝛥𝑡

𝐼 = 𝑛𝑞𝐴𝑣

𝑑

𝑉 = 𝐼𝑅

𝑅 =

𝜌𝐿

𝐴

𝜌 = 𝜌

0

( 1 + 𝛼𝛥𝑇)

𝑅 = 𝑅

0

( 1 + 𝛼𝛥𝑇)

𝑃 = 𝐼𝑉 =

𝑉

2

𝑅

= 𝐼

2

𝑅

𝑃

𝑎𝑣𝑒

=

𝐼

0

𝑉

0

𝐼

𝑟𝑚𝑠

=

𝐼

0

√ 2

𝑉

𝑟𝑚𝑠

=

𝑉

0

√ 2

Chapter 21: Circuits,

Bioelectricity, and DC

Instruments

𝑅

𝑆

= 𝑅

1

+ 𝑅

2

+ 𝑅

3

+ ⋯

𝑅

𝑃

=

𝑅

1

+

𝑅

2

+

𝑅

3

+ ⋯

𝑉 = 𝑒𝑚𝑓 − 𝐼𝑟

𝑉 = 𝑒𝑚𝑓 ( 1 − 𝑒

−

𝑡

𝑅𝐶 )

𝜏 = 𝑅𝐶

𝑉 = 𝑉

0

𝑒

−

𝑡

𝑟𝐶

Chapter 22: Magnetism

𝐹 = 𝑞𝑣𝐵 𝑠𝑖𝑛 𝜃

𝑟 =

𝑚𝑣

𝑞𝐵

𝜖 = 𝐵𝑙𝑣

𝐹 = 𝐼𝐿𝐵 𝑠𝑖𝑛 𝜃

𝜏 = 𝑁𝐼𝐴𝐵 𝑠𝑖𝑛 𝜃

𝐵 =

𝜇

0

𝐼

2 𝜋𝑟

𝐵 =

𝜇

0

𝐼

2 𝑅

𝐵 = 𝜇

0

𝑛𝐼

𝐹

𝑙

=

𝜇

0

𝐼

1

𝐼

2

2 𝜋𝑟

Chapter 23: Electromagnetic

Induction, AC Circuits, and

Electrical Technologies

𝛷 = 𝐵𝐴 𝑐𝑜𝑠 𝜃

𝑒𝑚𝑓 = −𝑁

𝛥𝛷

𝛥𝑡

𝑒𝑚𝑓 = 𝑣𝐵𝐿

𝑒𝑚𝑓 = 𝑁𝐴𝐵𝜔 𝑠𝑖𝑛 𝜔𝑡

𝑉

𝑆

𝑉

𝑃

=

𝑁

𝑆

𝑁

𝑃

=

𝐼

𝑃

𝐼

𝑆

𝑒𝑚𝑓

1

= −𝑀

𝛥𝐼

2

𝛥𝑡

𝑒𝑚𝑓 = −𝐿

𝛥𝐼

𝛥𝑡

𝐿 = 𝑁

𝛥𝛷

𝛥𝐼

𝐿 =

μ

0

𝑁

2

𝐴

ℓ

𝐸

𝑖𝑛𝑑

=

𝐿𝐼

2

𝐼 = 𝐼

0

( 1 − 𝑒

−

𝑡

𝜏 )

𝜏 =

𝐿

𝑅

𝐼 = 𝐼

0

𝑒

−

𝑡

𝜏

𝐼 =

𝑉

𝑋

𝐿

𝑋

𝐿

= 2 𝜋𝑓𝐿

𝐼 =

𝑉

𝑋

𝐶

𝑋

𝐶

=

2 𝜋𝑓𝐶

𝐼

0

=

𝑉

0

𝑍

𝑜𝑟 𝐼

𝑟𝑚𝑠

=

𝑉

𝑟𝑚𝑠

𝑍

𝑍 = √𝑅

2

+ (𝑋

𝐿

− 𝑋

𝐶

)

2

𝑓

0

=

2 𝜋√𝐿𝐶

𝑐𝑜𝑠 𝜙 =

𝑅

𝑍

𝑃

𝑎𝑣𝑒

= 𝐼

𝑟𝑚𝑠

𝑉

𝑟𝑚𝑠

𝑐𝑜𝑠 𝜙

Chapter 24: Electromagnetic

Waves

𝑐 =

√

𝜇

0

𝜖

0

𝐸

𝐵

= 𝑐

𝑐 = 𝑓𝜆

𝐼

𝑎𝑣𝑒

=

𝑐𝜖

0

𝐸

0

2

𝐼

𝑎𝑣𝑒

=

𝑐𝐵

0

2

2 𝜇

0

𝐼

𝑎𝑏𝑒

=

𝐸

0

𝐵

0

2 𝜇

0

Chapter 25: Geometric Optics

𝜃

𝑖

= 𝜃

𝑟

𝑛 =

𝑐

𝑣

𝑛

1

𝑠𝑖𝑛 𝜃

1

= 𝑛

2

𝑠𝑖𝑛 𝜃

2

𝜃

𝑐

= 𝑠𝑖𝑛

− 1

𝑛

2

𝑛

1

𝑃 =

𝑓

𝑓

=

𝑑

𝑜

+

𝑑

𝑖

𝑚 =

ℎ

𝑖

ℎ

𝑜

= −

𝑑

𝑖

𝑑

𝑜

𝑓 =

𝑅

Chapter 26: Vision and Optical

Instruments

𝑃 =

𝑑

𝑜

+

𝑑

𝑖

𝑚 = 𝑚

𝑜

𝑚

𝑒

𝑁𝐴 = 𝑛 𝑠𝑖𝑛 𝛼

𝑓/# =

𝑓

𝐷

≈

2 𝑁𝐴

𝑑

𝑖

= 𝑓

𝑜

𝑀 =

𝑓

𝑜

𝑓

𝑒

Chapter 27: Wave Optics

𝜆

𝑛

=

𝜆

𝑛

sin 𝜃 = 𝑚

𝜆

𝑑

𝑠𝑖𝑛 𝜃 = (𝑚 +

)

𝜆

𝑑

𝑠𝑖𝑛 𝜃 = 𝑚

𝜆

𝑊

𝜃 = 1. 22

𝜆

𝐷

2 𝑡 =

𝜆

𝑛

2 𝑡 = 𝜆

𝑛

I = ½ I 0

𝐼 = 𝐼

0

𝑐𝑜𝑠

2

𝜃

𝑡𝑎𝑛 𝜃

𝑏

=

𝑛

2

𝑛

1

Chapter 28: Special Relativity

𝛥𝑡 =

𝛥𝑡

0

√

1 −

𝑣

2

𝑐

2

𝛾 =

√

1 −

𝑣

2

𝑐

2

𝐿 = 𝐿

0

√

1 −

𝑣

2

𝑐

2

𝑣

𝐿𝐺

=

𝑣

𝐿𝑇

+ 𝑣

𝑇𝐺

1 +

𝑣

𝐿𝑇

𝑣

𝑇𝐺

𝑐

2

𝜆

𝑜𝑏𝑠

= 𝜆

𝑠

√

1 +

𝑢

𝑐

1 −

𝑢

𝑐

𝑓

𝑜𝑏𝑠

= 𝑓

𝑠

√

1 −

𝑢

𝑐

1 +

𝑢

𝑐

𝑝 =

𝑚𝑣

√

1 −

𝑣

2

𝑐

2

𝐸 =

𝑚𝑐

2

√

1 −

𝑣

2

𝑐

2

𝐸

0

= 𝑚𝑐

2

𝐾𝐸

𝑟𝑒𝑙

=

𝑚𝑐

2

√

1 −

𝑣

2

𝑐

2

− 𝑚𝑐

2

𝐸

2

=

(

𝑝𝑐

)

2

+

(

𝑚𝑐

2

)

2