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Disclaimer:
This lecture reviews some but not all of the
material that will be on the final exam that
covers in Chapters 29-33.
- LC circuit: Energy stored
- LC circuit: Oscillation frequency
- RLC circuit:
- With time varying emf
Chapter 29 Alternating-Current Circuits (1)
Resistance R Capacitive Reactance XC Inductive Reactance XL
- Time-varying emf
- Time-varying emf VR with resistor
- Time-varying emf VC with capacitor
- Time-varying emf VL with inductor
Chaper 29 Alternating-Current Circuits (2)
Summary: Phase and Phasors
Chapter 29 Alternating-Current Circuits (3)
Transformers Consider the second coil with NS turns The time-varying emf in the primary coil induces a time- varying magnetic field in the iron core. This core passes through the secondary coil Because both the primary and secondary coils experience the same changing magnetic field, we can write Thus a time-varying voltage is induced in the secondary coil described by Faraday’s Law step-up step-down
Chapter 29 Alternating-Current Circuits (4)
- Single loop RLC Circuit with time-varying emf:
- Phase constant:
- The average power
Chaper 29 Alternating-Current Circuits (5)
Resonance For given peak, R, L, and C, the current amplitude Ipeak will be at the maximum when the impedance Z is at the minimum. Resonance angular frequency: This is called resonance. i.e., load purely resistive ε and I in phase
Chaper 29 Alternating-Current Circuits (6)
Maxwell’s Equations Integral Form Differential Form where k = 2 / and = 2 f with wavelength and frequency f Wave solutions:
Chapter 31 Properties of Light (1)
- Law of Reflection:
- Focal length of a spherical miorr:
- Mirror Equation:
- Magnification:
- Law of Refraction (Snell’s Law):
- The critical angle for a total reflection: Laws of Reflection and Refraction: Summary Law of Reflection
- A reflected ray lies in the plane of incidence
- The angle of reflection is equal to the angle of incidence Law of refraction Indenx of refraction n:
- A refracted ray lies in the plane of incidence
- The angle of refraction is related to the angle of incidence by Snell’s Law Medium 1 where is the Medium i= wavelength in vacuum
Chapter 31 Properties of Light (2)
- The critical angle, c , at which total internal reflection takes place is given by
- Which we can rewrite as
- For n 2 = 1 (air)
- At angles less than c , some light is reflected and some is transmitted
- At angles greater than c , all the light is reflected and none is transmitted Total Internal Reflection air = 2 and nair =n 2 2 > 1 %
Chapter 31 Properties of Light (3)
Chromatic Dispersion The index of refraction of a medium is usually a function of the wavelength of the light. It is larger at shorter wavelengths. This causes spreading of light which is called chromatic dispersion. White light consists of components of nearly all the colors in the visible spectrum with approximately uniform intensities. The component of a beam of white light with shorter wavelength tends to be bent more. Spectrometer (such as a prism)
Chapter 31 Properties of Light (4)
Chapter 31 Properties of Light (6) Wave-Particle Duality of Light Refraction, diffraction (Huygens’s Principle) Interference (Young’s double slit interference) Electromagnetic waves (Maxwell’s Equations) Doesn’t require a medium Light and other EM radiation often come together (e.g., in Black-body radiation) Collisions, scattering as in photoelectric effect (Albert Einstein) Energy is quantized : Planck’s constant massless photons Quantum Mechanics: Duality for all particles Wave nature of light Particle nature of light
Chapter 32 Optical Images (1)
- Thin-Lens Equation:
- Lens-Maker’s Formula: Chapter 32 Optical Images (2) Mirror Equation and Magnification ( f = r/2 )
- Using these sign conventions we can express the mirror equation in terms of the object distance, do , and the image distance, di , and the focal length f of the mirror
- The magnification m of the mirror is defined to be ( f = r/2 ) Images Formed with Concave Lenses The image formed is virtual, upright, and reduced Chapter 32 Optical Images (3) Lens Equation
A capacitor in an LC circuit oscillator has a maximum potential difference of 15 V and a maximum energy 360 μJ. At a certain instant, the energy in the capacitor is 40 μJ. At that instant what is the potential difference across the capacitor? Example An AC generator producing 10 V (rms) at 200 rad/s is connected in series with a 50 ohm resistor, 400 mH inductor and a 200 μF capacitor. The rms voltage (in volts) across the resistor is: Example Consider a point (x,y,z) at -me t when Ex is nega-ve and has its maximum value. At (x,y,z) at -me t, what is By? A) By is posi-ve and has its maximum value B) By is nega-ve and has its maximum value C) By is zero D) We do not have enough informa-on Ex = E 0 sin(kz - wt)
Example UP (unpolarized light) TA LP E 1^ % E 2
I=I 0 %
I 1 =??
I 2 = Io/ TA LP n ˆ An unpolarized beam of light has intensity Io. It is incident on two ideal polarizing sheets. The angle between the axes of polarization of these sheets is . Find if the emerging light has intensity Io /4. Problem Example Example A laser beam of power 4.60 W and diameter 2.60 mm is directed upward at one circular face (of diameter less than 2.60 mm) of perfectly reflecting cylinder, which is made to “hover” by the beam’s radiation pressure. The cylinder’s density is 1.20 g/cm^3_. What is the height (in meters) of the cylinder?_
Example How thick is an anti-reflection coating for a glass lens which is chosen for light of wavelength 500 nm if the index of refraction of the coating is 1.29? Example How thick is an anti-reflection coating for a glass lens which is chosen for light of wavelength 500 nm if the index of refraction of the coating is 1.29? Example: Double Slit
d sin θ = m λ
sin θ ~ θ =
d
tan θ =
y
L
y = L tan θ = 1.68 mm
Example: Thin Film
