Untitled

• Medical Physics Course 2024/2025
• Classroom: Tacciuolo 14:00-16:00
• Date: 17-01-2025
• Differential and integral forms of electromagnetism equations are shown:

Gauss's Law for Electricity

• Differential form: ∇ ⋅ E = ρ/ε₀
• Integral form: ∯ E ⋅ dA = (Qenc)/ε₀

Gauss's Law for Magnetism

• Differential form: ∇ ⋅ B = 0
• Integral form: ∯ B ⋅ dA = 0

Maxwell-Faraday Equation (Faraday's Law of Induction)

• Differential form: ∇ × E = -∂B/∂t
• Integral form: ∮ E ⋅ dl = -(dΦB.S)/dt

Ampere's Circuital Law (with Maxwell's Correction)

• Differential form: ∇ × B = μ₀J + μ₀ε₀(∂E/∂t)
• Integral form: ∮ B ⋅ dl = μ₀Ienc + μ₀ε₀(dQenc/dt)

Resistors

• Resistors in series have the same electric current through all components
• Current amount is consistent through each resistor, regardless of resistance
• In a series circuit there is only one path for current flow
• Resistors in parallel, voltage across each component is the same, but current varies
• Total current divides among parallel branches according to individual branch resistance.

Resistors in Series and Parallel analysis

• Series: R(eq) = R1 + R2 + R3.
• Parallel: 1/R(eq) = 1/R1 + 1/R2 + 1/R3.

Light and Geometric Optics

• Light often travels in straight lines.
• Light is represented as rays, which are straight lines from an object.
• This is an idealization useful for geometric optics.

Reflection and Image Formation by a Plane Mirror

• Law of reflection: The angle of reflection equals the angle of incidence
• Diffuse reflection occurs when light reflects from a rough surface, causing the angle of incidence to vary
• Flat mirrors produce images that appear to be behind the mirror.

Index of Refraction

• Light slows down in a medium.
• The index of refraction is the ratio of the speed of light in a vacuum to the speed of light in a specific medium: n = c/v
• Vacuum: 1.0000
• Air (at STP): 1.0003
• Water: 1.33
• Ethyl alcohol: 1.36
• Fused quartz: 1.46
• Crown glass: 1.52
• Light flint: 1.58
• Acrylic, Lucite, CR-39: 1.50
• Polycarbonate: 1.59
• High-index: 1.6–1.7
• Sodium chloride: 1.53
• Diamond: 2.42
• λ is 589 nm

Refraction

• Light changes direction when crossing a boundary from one medium to another, which is called refraction.
• The angle that the outgoing ray makes with the normal is the angle of refraction.
• Snell's Law describes this phenomenon.

Snell's Law

• Snell’s Law Formula: n₁ sin θ₁ = n₂ sin θ₂
• n₁ is the index of refraction of the first medium
• θ₁ is the angle of incidence
• n₂ is the index of refraction of the second medium
• θ₂ is the angle of refraction.

Total Internal Reflection; Fiber Optics

• Total Internal Reflection: Light passing to a reduced refraction index leads to a larger refraction angle
• Critical Angle: The incidence angle that causes a 90° refraction angle
• Critical Angle Formula: sin θc = n₂/n₁ sin 90° = n₂/n₁
• Total Internal Reflection: the incidence angle is larger than the critical angle, no transmission ensues
• Fiber Optics: it transmits light, even when bent.
• Fiber Optics Applications: image creation using multiple small fibers for fiber-optic communication and medicine.
• Fiber-optic cables: They can carry over 100 separate wavelengths, transferring over 10 gigabits of data per second.

Thin Lenses; Ray Tracing

• Thin lenses have a small thickness relative to their curvature radius
• Thin Lens Types: converging or diverging. Their faces can be concave, convex, or plane.
• Converging lenses are thicker at the center
• Diverging lenses are thinner at the center

Lenses, Rays and Refraction

• Lenses use glass or transparent plastic with an air refraction index
• Snell's law applies where each ray experiences refraction.
• Converging Lenses: they focus parallel rays at a single point.
• Focal Length: the distance from the converging lens's center to the focal point.
• Lens Power Formula: P = 1/f
• The unit for lens power is diopters (D), where 1 D = 1 m⁻¹

Human Eye

• Human Eye Similarities: the eye functions like a camera with iris, adjustable lens and retina

Structure of Human Eye

• Vitreous Humor: gel with n=1.337.
• Iris: acts as a diaphragm that is colored
• Pupil: hole in the iris for light passage.
• Retina: sensor/film equivalent.
• Cornea: surface (n=1.376) refracts light where it interfaces with air
• Lens (n=1.386 to 1.406): adjusts to focus at varying distances

Corrective Lenses

• Diverging Lenses: correct nearsightedness. Power is specified in diopters (P = 1/f).
• Converging Lenses: correct farsightedness and specified as P = 1/f in diopters.
• Underwater Vision: blurry due to reduced light bending. Goggles correct this

Electromagnetic Fields

• Lorentz Force
• The equation shows electric force (qE) and magnetic force (qv × B)
• The electric force points in the same direction as the electric field
• The electric and magnetic fields are perpendicular to the velocity of the particle
• gamma ray
• X-ray
• ultraviolet
• visible light
• infrared
• microwave
• radio
• shorter wavelength, is higher in frequency and higher in energy
• longer wavelength, is lower in frequency and lower in energy

Oxygen Saturation

• The fraction of oxygen-saturated hemoglobin relative to total hemoglobin in the blood
• The body regulates oxygen balance precisely.
• Normal is 95%
• Below 80% may compromise organ function and should be addressed

LASER

• Light Amplification by Stimulated Emission of Radiation

Radiation and Atom Interactions include

• Spontaneous Emission: Energy of the emitted photon represented as hf = ΔE
• Stimulated Emission: One photon interacts and produces two with the same properties
• Absorption: the light particle (photon) is absorbed

Atomic Transition

• Spontaneous emission is defined by constant 𝑣₀=(𝐸₂−𝐸₁)/ℎ

For Spontaneous Emission process has probability to occur

• (𝑑𝑁₂/𝑑𝑡)sp=−𝐴𝑁₂
• Spontaneous: represented as A: Einstein A coefficient.
• Radiative Lifetime: defined as 𝜏sp=1𝐴

Laser Energy

• 3 Levels of Energy involved (He-Ne)
• N2 > N1

Laser Elements

• Totally reflecting mirror (R = 100%)
• Active medium
• Partially reflecting mirror (R < 100%)
• Excitation mechanism
• Laser optical cavity

Laser Properties

• Monochromatic: Concentrated in a narrow wavelength range/specific color.
• Coherent: Emitted photons maintains phase relationship in time and space.
• Directional: Extremely focused, strong beam.

Radio Waves for Mobile Phones and Heating

• Mobile phones use microwave energy, causing the possibility of heating.
• Brain temperature increases by about 0.2°C with mobile phone use.

X-Ray Tubes

• Cathode
• Anode
• Tube emits photons and electrons

Radiography

• Shows X-rays absorbed by dense parts of a body/patient
• Photographic plate or digital detector processes the image
• Radiographs appear white in dense areas of the body, gray in less dense regions

LINAC

• Linear Accelerator to generate radiation therapy
• Uses Electron Gun
• Accelerating Waveguide
• 270° Bending Magnet
• X-ray Target
• Gantry (Axis)
• Isocenter
• Treatment Couch