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In this section, we study the reflection of light, focusing on how light is reflected in
The law of reflection states that the angle of incidence is equal to the angle of reflection. Remember that the angles are measured relative to the normal line. More...
From what we learned from the section on "Electromagnetism", we know that: 1) a changing electric field should create a magnetic field, and 2) a changing magnetic field can create an electric field.
An electromagnetic wave is a combination of electric and magnetic fields that vibrate together in space and time in a synchronous fashion and propagate through space (even vacuum) at the speed of light.
The electromagnetic wave is a transverse wave.
The electric and magnetic fields oscillate in the direction perpendicular to the direction of propagation.
The EM wave propagates because the electric field recreates the magnetic field and the magnetic field recreates the electric field.
Electromagnetic waves also experience the Doppler effect. As with sound, motion towards corresponds to a frequency shift upward and a wavelength shift downward, and motion away corresponds to a frequency shift downward and wavelength shift upward (the so-called red-shift).
For example, suppose we observed the light from a distant galaxy is received on Earth with a wavelength of 650nm. But it is known that the wavelength of this light upon emission was 625nm. Then we should know that this galaxy is receding from Earth.
Light is an electromagnetic wave –has both electric and magnetic parts and does not require a medium. A medium is any physical substance through which energy can be transferred. There are different types of electromagnetic waves, depending on their frequency levels and energy levels. Electromagnetic waves are formed when an electric field (shown as blue arrows) couples with a magnetic field (shown as red arrows). The magnetic and electric fields of an electromagnetic wave are perpendicular to each other and to the direction of the wave. Electromagnetic Waves have different wavelengths. When you listen to the radio, watch TV, or cook dinner in a microwave oven, you are using electromagnetic waves. Radio waves, television waves, and microwaves are all types of electromagnetic waves. They differ from each other in wavelength. Wavelength is the distance between one wave crest to the next. More...
The laws of physics are the same in all inertial frames of reference. No physics experiment can ever determine whether you are at rest or moving at a constant velocity.
There is at least one inertial frame of reference in which, for an observer at rest in this frame of reference, the speed of light, c, in a vacuum is independent of the motion of the source of the light.
First, think of the following experiment: to A and to B, will the baseball reach the front and back of the traincar at the same time?
Observer A is standing in the middle of moving traincar, which passes Observer B who is standing on the platform of a train station. The traincar is moving at speed Vt
Observer A throws a baseball at the front, and another baseball at the back, of the traincar at the same time, with the same speed Vb, just as the two observers pass each other. For the observer on board the train, Observer A, the front and back of the traincar are at fixed and equal distances from where he stands and as such, according to this observer, the ball will reach the front and back of the traincar at the same time.
For the observer standing on the platform, Observer B, on the other hand, the rear of the traincar is moving (catching up) toward the point at which the baseball was thrown, and the front of the traincar is moving away from it, both with a speed of Vt. The ball thrown at the front is moving toward the front at a speed of Vb+Vt, and the ball thrown at the rear is moving at a speed of Vb-Vt. In the meantime, the ball thrown at the rear will have less distance to travel than the ball thrown at the front. The speed of the moving traincar will then cancel out when Observer B is calculating when the baseball will reach the back and when it will reach the front of the traincar. So even to him, the ball will reach the front and the back at the same time, same conclusion as Observer A.
Now, let's replace the baseball with a flash light, and see what will happen.
A flash of light is given off at the center of the traincar just as the two observers pass each other. For the observer on board the train, Observer A, the front and back of the traincar are at fixed distances from the source of light and as such, according to Observer A, the light will reach the front and back of the traincar at the same time.
For the observer standing on the platform, Observer B, on the other hand, the rear of the traincar is moving (catching up) toward the point at which the flash was given off, and the front of the traincar is moving away from it. The speed of light is finite and the same in all directions for all observers (The Speed of Light Principle), and the light headed for the back of the train will have less distance to cover than the light headed for the front. Thus, to Observer B, the flashes of light will strike the rear of the traincar before it strikes the front of the traincar. This is a different conclusion than Observer A's conclusion.
Notice how the “principle of the Speed of Light” made a difference in the answers to above questions.
Simultanuity refers to the occurrence of two or more events at the same time. Your everyday experiences suggest that the notion of simultanuity is absolute: ie, 2 events ar either simultaneous or not simultaneous for all observers. However, this is not the case in the world of special relativity. Let's review the following thought experiment:
In the diagram below, Observer 1 is standing in the middle of his railway car, moving with a speed v relative to observer 2, when 2 lightning bolts strike the ends of the car. The lightning bolts leave burn marks on the ground at point A and B, which also indicates the 2 ends of the railway car when the lightning strikes.
Did the 2 lightning bolts strike simultaneously?
To Observer 2, she is standing midway between the burn marks at A and B. The light pulses from the lightning bolts reach her at the same time.
To Observer 1, he is standing in the middle of his railway car when lightning strikes, so he is also midway between the 2 places where the lightning bolts strike. The light pulses from the lightning bolts reach him at the same time.
However, to Observer 2 who is watching Observer 1's moving railway car, she notices that Observer 1 is moving with his railway car to the right toward point B and away from point A. Therefore, Observer 2 concludes that Observer 1 should see the lightning strikes point B before it strikes point A.
To Observer 1 who is watching Observer 2, he notices Observer 2 is moving (relative to his railway car) toward point B and away from point A. Therefore, Observer 1 concludes that Observer 2 should see the lightning strikes point A before it strikes point B.
Conclusion: The observation of simultanuity is different in different frames of reference.
A light clock is travelling with observer 1 on his raiway car. Light pulses travel back and forth in the clock. Each tick of the clock takes a time Δts = 2d/c. According to observer 1, the operation of the clock is the same whether or not the railway car is moving.
Observer 2, who is at rest on the ground, views the motion of the light pulses in the clock and sees the light pulse move a greater distance. Thus to her, time slows according to observer 1's light clock. To her, each tick of observer 1's clock takes a time Δtm
In the above experiment, Δts is called "proper time", which refers to the time interval measured by an observer at rest with respect to a clock.
Using the same example as in “Time Dilation”. Suppose observer 2 marks 2 locations A and B on the ground. She then tries to measure the distance between A and B, Ls, using the light clock on observer 1’s railway car.
Now, for observer 1, when he measures the distance between A and B, his measurement will come to be
Lm = vΔts
This means:
And obviously,
Ls > Lm
In above experiment, Ls is called “proper length”, which is the length of an object or distance between 2 points as measured by an observer who is stationary relative to the object or distance. Lm is called “relativistic length”, which is the length of an object or distance between 2 points as measured by an observer moving with respect to the object or distance.
Meons are particles that are about 207 times as massive as electrons, travel at speeds of about .99c, and decay in 22ms for an observer at rest relative to the muons.
Muons can come from the cosmic radiation that collides with atoms in Earth's upper atmosphere. In Newtonian mechanics, most of these meons should decay after travelling about 660m into the atmosphere. Yet experimental evidence shows that a large number of muons decay after travelling 4800m - over 7 times as far.
Why?
To observers on Earth, meons undergo time dilation as muons travel at very close to speed of light. Due to time dilation, muons' "clocks" run slower relative to Earth clocks, so their lifetimes increase by a factor of 7. That is why they can travel a greater distance.
To observers travelling with muons, the Earth is undergoing a length contraction. The distance from the upper atmosphere to Earth's surface appear to be about 1/7 its normal thickness. Thus while the muons decay in their own frame of reference in just 2.2ms, the 4800m distance they mst travel shortens in their frame of reference to 660m.
The twin paradox refers to a thought experiment in which a traveller in one frame of reference returns from a voyage to learn that time had passed more slowly in his spacecraft relative to the passage of time on Earth. This actually does not contradict the special relativity theory. This is because the special relativity theory is only applicable to inertia frame of references where all objects are either at rest with each other or in constant motion with each other. In order for the spacecraft to come back, the spacecraft must have changed its velocity - direction and/or magnitude - which will make the special relativity theory no longer applicable.
Newtonian mechanics predicts that momentum increases linearly with speed (p = mv), while special relativity theory predicts that relativistic momentum approaches infinity at speeds close to c (speed of light).
In above equation, the relativistic mass:
The mass of an object measured at rest with respect to the observer will not change and is called "rest mass" or "proper mass". But the "relativistic mass" as given above, measured by an observer moving with speed v with respect to the object, will approach infinity at speeds close to c.
According to Special Relativity Theory, there is a universal speed limit and that is the speed of light in vacuum c. This is because if object speed v goes to or above light speed c, the expression
will be invalid when used as denominator in above equations.
In Einstein's energy-mass equation:
Erest = mc2
Where Erest is the energy of an object that is at rest with respect to an observer.
When an object is in relative motion with an observer, its total energy will be larger than its rest energy:
The extra energy is the relativistic kinetic energy Ek:
The minimum energy needed to remove an electron bound to a metal surface. Work function Φ = hf0
Experiments with different metals show that though different metals have different threshold frequencies and therefore different work functions, they all obey the same photoelectric equation and have the same slope h.
We can prove why Pphoton = Ephoton /c:
Total energy Etotal
Relativistic momentum p
For photon, v = c, so Pphoton = E/c
When a photon comes into contact with matter, the interaction obeys law of conservation of momentum, and has 5 different results:
When a photon comes into contact with matter, the interaction may cause a photon to emerge with less energy and momentum after freeing an electron. After this interaction, the photon still travels at the speed of light but with less energy and a lower frequency. In the photoelectric experiment, it is observed that scattered photon has lower frequency and therefore lower energy.
When you do double-slit experiment with particles such as tennis balls, they do not show interference effects.
When you do double-slit experiment with light, you see constructive and destructive interference produces bright and dark fringes on the screen.
When you do double-slit experiment with electrons, you see they produce the same constructive and destructive interference pattern on the screen as light.
The double-slit experiment with quantum objects such as electrons and electromagnetic radiation such as light suggest that they have both wave-like and particle-like behavior - wave-particle duality:
From the photon momentum equation Pphoton = h / λ (h is planck’s constant and λ is wavelength), we have
λ = h / Pphoton
To extend above to all classical particles, we have
λ = h / P = h / mv
The wavelength above that is associated with the motion of a particle (photon, electron, etc.) with momentum p is called the de Broglie wavelength. If a particle has a wavelength, the particle should exhibit interference as waves do. When particles are large, wavelength will be so small you will not see the wave; when particles are small at atomic level, you see wave like properties as in light and electrons.
Heisenberg Uncertainty Principle says that there is a limit to how accurately simultaneous measurements of the position and momentum o f a quantum object can be. This is expressed as a mathematical statement that says that if Δx is the uncertainty in a particle's position, and Δp is the uncertainty in its momentum, then
ΔxΔp >= h / (4π), where h is planck’s constant.
Heisenberg Uncertainty Principle can be used to explain the double slit experiment of electrons. When an electron passes through a wide slit (large position uncertainty), the diffraction spot on the screen is narrow (small momentum uncertainty). When the slit is narrower (smaller position uncertainty), the diffraction spot becomes wider (larger momentum uncertainty).
What is a black body? Black body is a kind of objects that do not reflect light. Black body objects absorb all incident light. There is no perfect black body in the world, but examples of objects that are close to black body are the sun, your black T-shirt, a pizza oven burning charcoal, etc.
When will a black body radiate electromagnetic waves? When its inside temperature heats up.
Wien’ law
According to Wien's law, as temperature heats up, an ideal blackbody will emit electromagnetic waves at different wavelengths. And as blackbody temperature increases, the wavelength at whcih the radiation intensity is largest, λmax, will become shorter and shorter, given by the equation below (another way to summarize Wien's law is: peak wavelength is inversely proportional to temperature):
λmax = (2.90 x 10-3 mK) / T, where T is blackbody temperature in Kelvin, and 2.90 x 10-3 mK is Wien's displacement constant (in meter kelvin).
Ultraviolet Catastrophe
The Wien's law predicts that as temperature increases, peak wavelength will keep shifting to the left. However, this is not what the experiment has found out. The blackbody experiment has shown that the intensity would dip down to the left of the UV portion of the spectrum, as temperature increases. (for more detailed explanation, refer to https://www.youtube.com/watch?v=7BXvc9W97iU)
Planck's Math Formula
The spectral radiance of a body, Bν, describes the amount of energy it gives off as radiation of different frequencies. It is measured in terms of the power emitted per unit area of the body, per unit solid angle that the radiation is measured over, per unit frequency. Planck showed that the spectral radiance of a body for frequency ν at absolute temperature T is given by
The above formula can fit the blackbody experiment results very well. But what is more important about Planck's blackbody formula for Quantum Physics is that in order to use the formula, you need to accept Planck's hypothesis that
For more detailed explanation, you can refer to https://m.youtube.com/watch?v=7hxYGaegxAM
More...According to Rutherford's planetary model of the atom, electrons orbit the nucleus under the influence of the elctric force. For example, in a hydrogen atom, an electron with charge -e orbits a proton with charge +e.
Rutherford established his model of atom by doing an experiment with alpha particles. He fired alpha particles at an extremely thin sheet of gold foil. While most alpha particles sailed right through the target gold atoms, a small percentage of the alpha particles were deflected through very large angles (90° to 180°). These alpha particles hit the nucleus of the gold atoms and were thus deflected.
The problem with the planetary model of the atom is that the radiation emitted by an orbbiting electron, as predicted by Maxwell's theory, would result in the electron losing energy and spiralling into the nucleus.
The main ideas of Bohr model are these:
The energy levels within an atom are given by the following formula:
En = (Z2/n2) x (-13.6 eV), where 1 eV = 1.6 x 10-19 J, Z is number of protons in the atom's nucleus.
The Bohr model of atom can be used to explain the phenomenon known to physicists that atoms emit or absorb radiation only at certain discrete wavelengths.
The problem with the Bohr model of atom is that it works with hydrogen atom, but it does not work well with atoms with many electrons.
Refer to this video: https://m.youtube.com/watch?v=KgcqjILr97E
Mass of He nucleus < combined mass of 2 protons and 2 neutrons - the difference is the mass defect.
If we combine protons and neutrons into He, some mass will be converted into energy in accordance with E = mc2
According to the binding enery curve:
Watch this video for a detailed discussion: https://m.youtube.com/watch?v=fES21E0qebw
Half life is the time required for half of a given sample to decay.
Here is 1 possible uranium fission reaction equation:
Here is 1 hydrogen fussion reaction, the one that powers the Sun:
Note in above reactions equations, the energy component is called "disintegration energy", and is usually denoted by letter Q. Q can be positive (as in above nuclear fission and fusion reactions), or negative. If disintegration energy Q is positive, the reaction is "exothermic" and can occur spontaneously; If disintegration energy Q is negative, the reaction is "endothermic", and cannot occur spontaneously.
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Volume of cube = s3 where s is the length of any edge of the cube.
The gas theory works on the following assumptions:
The ideal gas law can be explained with the equation: More...
Virtual Image is an image formed by light coming from an apparent light source; light is not coming from the actual image location (actual light source).
A force is a push or pull upon an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects. When the interaction ceases, the two objects no longer experience the force. Forces only exist as a result of an interaction.
All forces (interactions) between objects can be placed into two broad categories: More...
Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance.
Velocity is a vector quantity that refers to "the rate at which an object changes its position." Velocity can be thought of as the rate at which an object covers displacement. Imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. While this might result in a frenzy of activity, it would result in a zero velocity because this person has had 0 displacement.
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