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Geometric optics, lenses, mirrors, relection, refraction, focal point, focal length, total internal reflection, index of refraction, lens power, combinations of lenses

Equations:

The index of refraction n determines the speed of light v in a medium according to

Light passing from one medium to another obeys Snell's Law:

Total internal reflection occurs when light passes from a medium 1 with a higher index of reraction to a medium 2 with a lower index of refraction, if the angle is greater than a critical angle

The thin lens equation relates the distances to the image and object, d_i and d_o to the focal length f according to

The distance to the object and image are positive if they are real, and negative if they are virtual. The focal length is positive for converging lenses and negative for diverging lenses.

The same equation applies to a mirror, with the focal length related to the radius of curvature r by

The magnification of a lens or mirror is the ratio of the height h_i of the image to the height h_o of the object, and is given by

For combinations of lenses, the object position for the second lens is the image position for the first lens.

Cameras, the eye, magnifiers, telescopes, microscopes, aberration, diffraction limits.

Equations:

Cameras: The f-stop of a lens depends on its focal length and diameter. The amount of light admitted by the lens is proportional to the square of the diameter, so it is inversely proportional to the square of the f-stop.

Eyes: Nearsightedness can be corrected by a diverging lens whose focal point is at the furthest point where the eye can naturally focus when relaxed. Farsightedness can be corrected with a converging lens which put the image of an object 25 cm away at the location of the eye's actual near point, which is further away. The thin lens equation is used in either case to find the focal length needed.

Magnifier: The magnification with the image at infinity is

In a telescope, parallel rays from a distant object are focused at the focal point of the objective lens, which is in turn the focal point of the eyepiece. Parallel rays then go to the eye, which sees the object at infinity.

Telescope with objective focal length f_o and eyepiece focal length f_i has magnification:

In microscopes, the object is placed just beyond the focal point of the objective lens, producing an enlarged image at the focal point of the eyepiece, which acts as a magnifier to produce an image at infinity. The magnification of the objective lens is

The size of a lens aperture limits the resolution due to diffraction through the opening, which creates a peak whose half-width (width to first minimum) is

If a material of index of refraction n fills the space below the objective lens, the resolving power is smaller by a factor of 1/n, because the wavelength is increased by a factor of n compared to in a vacuum.

Units:

1 Diopter = 1 m^-1 in inverse focal length

The principle of relativity (physics is the same in all intertial frames), constancy of the speed of light in a vacuum, simultaneity, time dilation, length contraction, mass increase, relations between energy and momentum, addition of velocities.

Equations:

Let g = (1-v²/c²)^-1/2. This factor is always greater than 1, and represents the time dilation factor by which events happen more slowly in a moving reference frame. A person taking a trip on a fast rocket will age more slowly by this factor. The mass of a moving object will increase by the same factor, and its length will decrease by this factor, becoming L / g.

The relativistic momentum is

The kinetic energy of a moving object is

The total relativistic energy satisfies

The relativistic sum of parallel velocities u and v is

Convenient units for masses of relativistic particles are eV/c². Convenient units of momentum are eV/c. For higher energies, substitute keV, MeV, ... as needed.

Discovery of the electron, blackbody radiation and Planck's quantum hypothesis, the photoelectric effect and photons, photon interactions, wave-particle duality, the wave nature of matter (de Broglie waves), electron microscopes, early models of the atom, atomic spectra, the Bohr atom.

Equations:

There are many equations in this chapter. This review lists the most important of them.

Wien's Law says that the peak wavelength l_P emitted by a blackbody (perfect emitter or absorber) is related to its absolute temperature T by

Planck's quantum hypothesis says that molecular or atomic vibrations have a minimum energy related to their frequency f by E_min = hf with Planck's Constant h = 6.626 x 10^-34Js.

Photons are the basic particle constituents of electromagnetic fields. they carry energy

In the photoelectric effect, if is initially bound with a potential energy -W, which requires work W to overcome, then it is ejected from an atom with kinetic energy

de Broglie suggested that the relation between momentum and wavelength of photons applies to all objects: they have a wavelength related to their momentum by

Electron microscopes use the short wavelength of electrons to probe smaller objects than optical microscopes can.

The spectral lines of hydrogen have wavelengths given by the Rydberg law

The spectral lines of single-electron atoms can be found using Bohr's quantum condition

The quantized energy levels are given by

The spectral lines occur when the photon has an energy which is the difference between two of these quantized energy levels:

Quantum Mechanics, Heisenberg uncertainty principle, probability distributions, quantum numbers, Zeeman effect, fine structure, Pauli exclusion principle, shells and subshells

Equations:

Quantum numbers: n, l, m_l, m_s

• n is the principle quantum number, with values 1, 2, 3, ... as in Bohr atom.
• l is the orbital quantum number, which determines the angular momentum of the electron. It has values from 0 to n-1.
• m_l is the magnetic quantum number, related to the direction of the angular momentum. It runs from -l to l, and the corresponding energy levels are split in a magnetic field. This is called the Zeeman effect.
• m_s is the spin quantum number. It has two values, +1/2 or -1/2, corresponding to "spin up" or "spin down". The spin is responsible for fine structure in the atomic spectrum.

In multi-electron atoms, orbitals are filled from the most tightly bound to the least tightly bound following the Pauli exclusion principle: no two electrons can occupy the same quantum state (ie, have the same quantum numbers).

Electrons with the same principle quantum number n are said to be in the same shell. Electrons with the same n and l are in the same subshell. Subshells are labelled s, p, d, f, ... for l = 0, 1, 2, 3, .... The periodic table shows the arrangement of atoms according to what shells and subshells are filled.

Concepts:

Nuclear physics, nuclides, isotopes, radioactive decay, alpha decay, beta decay, gamma decay, protons, neutrons, neutrinos, strong and weak nuclear force, decay constant, half-life, activity

Equations:

The atomic mass number A is the number of protons plus neutrons in a nucleus. The atomic number Z is the number of protons in a nucleus.

An isotope X with mass number A and atomic number Z is written as ^A_ZX.

The difference between the mass of a nucleus and the mass of the constituent nucleons is the nuclear binding energy.

Masses of nuclides are normally given for neutral isotopes, and include the mass and binding energies of enough electrons to balance the nuclear charge. The binding energies of the electrons normally do not make a significant contribution to the nuclide's mass, but the mass of the electrons generally cannot be neglected.

The number of nuclei DN which decay in a time Dt is proportional to the number N of nuclei present and a decay constant l:

Units:

Nuclear masses are expressed in terms of unified atomic mass units (u) in which ¹²₆C has exactly mass 12 u.