SAT II Subject Test Physics: Thermal Physics/Thermodynamics - Heat and Temperature

• Molecules
All matter is composed of molecules that are relatively far apart and exert force on each other only when they collide.
• Pressure of Gas
The pressure of gas is caused by collisions of gas molecules with the walls of the container.
• Compare to gas, molecules of liquids are comparatively close to each other, in solid the molecules are much closer together, there are considerable bonding force between the molecules.
• temperature is a measure of the average kinetic energy per molecule of a substance
The above definition may sound strange to you and me, but hey this is science and it can be nerdy.
• The average kinetic energy of the oxygen molecules is the same as that of the hydrogen molecules. However oxygen molecule will move more slowly because oxygen molecule has greater mass based on kinetic energy formula:
  
• Standard pressure is the pressure that would be produced by a column of 76cm high mercury
• Kelvin scale is used as an absolute temperature scale and this scale has no negative temperatures. The absolute zero is the coldest temperature in theory.
  
• Expansion and contraction
When solid is heated, it expands in length, area and volume
• If a hollow solid (e.g. a coin with a hole in the middle) is heated, the empty space increase in volume just as though it were made of the same material as the solid.
• As water is cooled from 100 °C, it contracts until is reaches 4 °C. Then it expands if it is cooled further.
  
• If the pressure on a gas is kept constant, heating the gas will result in an increase in its volume
  
  1. Charles' law
  If the pressure on a gas is kept constant, its volume is directly proportion to the absolute temperature
  
  2. Boyle's law
  If the temperature of a gas is kept constant, it volume of the gas varies inversely with the pressure
  
  3. General Gas Law (combines Charles' law and Bayle's law)
  
  4. SI unit for pressure is Pascal
  One Pascal is 1 Newton per square meter
• "Internal energy" or "work" or "heat being transferred" are all measured in "Joules"
Food contains energy and this is also officially measured in "Joules". Most people are familiar with calorie, which is a pre-SI metric unit of energy. One "Calorie" approximates the energy needed to increase the temperature of 1 gram of water by 1 °C, which is about 4.2 Joules. Check the food label of your grocery and you are most likely to find energy measured in both Calorie and Jules.

• Specific Heat Capacity (sp. ht.)
Specific heat capacity of a substance is the amount of heat required to raise the temperature of 1gram of the substance by 1°C.
• Specific heat capacity of solid is different from the liquid form of the same substance, eg.
Heat capacity of ice is: 2.05 joules/g.°C Heat capacity of water is: 4.19 joules/g.°C
• Change of phase
During the change of phase, heat represents an increase in potential energy rather than kinetic energy. Therefore the temperature remains the same.
• During heat transfer, heat lost by the hot object = heat gained by the cold object
• Heat of fusion of a substance is the amount of heat required to melt a unit mass of the substance without changing of temperature
• Melting point is practically independent of atmosphere pressure
• Boiling point is normally directly related to the atmosphere pressure, in the high mountains, where the atmosphere pressure is lower, the boiling point of water is much lower than on the ground
• Regelation
Regelation is melting under increased pressure (melting point is lower than usual) and refreezing when the pressure is reduced. This only occurs when substance, such as ice that expands upon freezing. You can observe this with ice skating. The melting point change is normally very small compared to the pressure change. E.g. for ice to melt at -4°C rather than 0°C, 500 atmosphere pressure is required.
• A lower melting point can also be resulted from dissolving solids in the liquid. E.g. 10% salt solution melt at -6°C and 20% salt solution melt at -16°C. That is why you sometimes see worker add salt on the road to help melting the ice.
• Evaporation
Evaporation is a cooling process with fast moving molecules at the surface escape from the liquid
• Boiling
Heat of vaporization of a substance is the amount of heat needed to vaporize a unit mass (1g) without changing its temperature.
• Effect of pressure increase
Boiling point decrease Melting point changes very little
• Sublimation
Substance changes directly from solid to vapor without going through liquid phase
• Condensation
Change from vapor to liquid, occasionally used to refer to the reverse of sublimation that is the direct conversion of a vapor to a solid (e.g. frost)

SAT II Subject Test Physics: Geometrical Optics - Common applications

• Sight Correction Lenses
  
  1. Nearsighted people need to wear concave lenses because for them the image of an object is brought into focus too soon (in front of the retina)
     
  2. farsighted people need to wear convex lenses because for them the image of an object is brought into focus beyond the retina.
     
  
• Understand lens f-numbers
f/8 means the diameter of the lens is 1/8 of the focal point
• Understand the principle of astronomical telescope and compound microscope
  
  1. Telescope magnification =
     (focal length of the object)/(focal length of the eyepiece)
     
  2. Microscope magnification =
     (power of eyepiece) x (power of object piece)
     
• What is monochromatic light
The light that has one single color
• What is chromatic aberration
The focal length of a lens varies upon the color of light.
• Fraunhofer lines in Sun's spectrum are produced mostly by the gases in Sun's atmosphere that absorb some of the energy emitted from the hot core
  

SAT II Subject Test Physics: Geometrical Optics - Critical angle and Total reflection

Total reflection can only occur when the light is traveling from denser medium to rarer medium. From water to the air for example. A good excuse to buy a water proof torch that you can experiment in the swimming pool. :)

When light travels between two different medium, both reflection and refraction occur normally. Since the light is traveling from denser medium to the rarer medium, the angle of refraction will be greater than the angle of incident. We can however found an angle of incident that the angle of refraction becomes 90 degree, i.e parallel to the surface. In this case, no refraction occurred, all lights are reflected. This is called total reflection and the incident angle at that point is called critical angle.

In summary, when the incident angle is 0, not reflection occurs, it is total refraction. However when the incident angle reach the critical angle, no refraction occurs, it is total reflection. When the incident angle is between 0 and critical angle, the greater the angle of incidence, the greater the amount of reflection.

SAT II Subject Test Physics: Geometrical Optics - Some facts to remember

• Index of refraction of a medium
  n = (speed of light in air)/(speed of light in the given medium)
  
• If light goes through parallel surface of a transparent substance such as flat glass the emerging ray is parallel to the entering ray. The incident ray is refracted entering the glass bending towards the normal and then bending away from the normal when refracted again into the air. As a result the emerging ray is parallel to the enter ray.
  
• Rainbow colors we see in nature world and their optics characters

Infrared light has a greater wave length than red, ultraviolet has a shorter wavelength than violet, both not visible to human eyes, but used very commonly in industrial applications
• In vacuum all electromagnetic waves travel at the same speed
• If an object reflects no light, it is said to be black, if an object reflects all colors, it is show as white and if a white object exposed only to red light, it will appear as red. However on the other hand if a red color object is exposed by only blue light, it will show as black because the color of an opaque object is determined by the color of the light it reflects.
  
• Primary colors: Red, Green and Blue-violet
  If we mix two primary colors, we get the complementary color of the third one.
  
• Mixing primary color and its complementary color produces white color
  
  1. Red and blue-green
  2. yellow and blue-violet
  3. green and magenta (purple)
  The above is talking about color of light and don't get confused with mixing paint. Paint absord light and are seen as the color it reflects
• Resolving power of lenses
The imaging system's resolution can be limited either by aberration or by diffraction causing blurring of the image. A lens with a larger diameter will decrease the amount of the diffraction and increase the resolving power.
• Polarization
Polarized light is light whose direction of vibration has been restricted in some way. Please remember light is a transverse wave and only transverse wave can be polarized. Longitudinal wave can't be polarized.
• What is laser
Laser stands for "Light Amplification by Stimulated Emission of Radiation". Lasers are devices that produce monochromatic and coherent beams of light. The beam is very highly collimated (whose rays are nearly parallel, and therefore will spread slowly as it propagates), it has a very high energy density.
• Maxwell's theory
Light is transverse wave in which electric and magnetic fields vibrates or fluctuate at right angles to the direction of propagation.
• Doppler effect of light
We are all very familiar with doppler effect of sound waves. When the object that producing the sound wave is getting closer, the observed frequency is higher than the source. Doppler effect is common in all waves, just just sound. Light exhibits doppler effect as well even though it is much less noticed. LIDAR speed gun is an application that based on doppler effect of laser. I know all these science stuff are boring and people are making fun of it. If you like Physics, you probably watch "Big Bang Theory" and you certainly remember this one.

Or you can watch it on Youtube: You Tube.
• Explain why we can see a lot of colors with a thin film
This once again demonstrate the wave character of light.

SAT II Subject Test Physics: Geometrical Optics - Reflection and Refraction: Q & A

Q & A is the best way for parents to help a student to review the topic. It is interactive, fun and you will most likely learn something in the process too. As for the student, often than not, (s)he will pickup something that (s)he didn't understand clear enough to say it in his own words.

1. The most common questions on "Geometrical Optics" is about the image formed from a mirror and lens, it can be a question on
• real image vs virtual image
• the image is upright/erect or inverted?
• the image is smaller or bigger than the original image?
You can of course use mirror equation and lens equation as shown below. However it is sometime confusing as whether a positive or negative value should be used. So I strongly recommend you to use a simple drawing to verify your answer from using the equation.

Some facts to remember
1. Which side is the real image?
For mirrors, the real side is the same side as the object. For lenses, the real side is the opposite the object. Think of a projector.
2. Convex/Diverging lens can only form a virtual image and it is always smaller than the real image. If your eyes are shortsighted, try your glasses
3. For convex/converging lens
Virtual image is always larger, however real image can be larger or smaller.

Object to the center	Image
Between f and 2f	real, magnified, inverted, think of a projector lens
Greater than 2f	real, smaller, inverted
Less than f	Virtual, magnified, upright, think of a magnifying glass or reading glass

SAT II Subject Test Physics: Geometrical Optics - Reflection and Refraction: Concepts

We started our notes with this only because my son learned very little at school on this subject and he felt least confident on this in the exam.

If you have read through the text in both "Princeton Review" and Barron's book on this topic, you should be familiar with the key words or terminologies listed below. If you are a parent, you can test your son or daughter's understanding by asking, e.g. "what is the angle of incident?". You can even ask him/her to draw on the paper. Without knowing the accurate definition of these terms, answering the questions can become tricky even if you do understand the concept.

1. Normal
The normal is a line perpendicular to the interface, the surface boundary of two medium

2. Angle of Incidence
The angle that the incident beam makes with the normal

3. Angle of Reflection
The angle that the reflected beam makes with the normal

4. Angle of Refraction
The angle that the transmitted (refracted) beam into the new medium makes with the normal

5. Diffraction
When a wave encounters a slit with a width that is comparable with the wavelength, the wave will fan out after it passes through Single slit and double slits experiments are used to demonstrate that light has wave characters.
6. diffraction gratings
Barriers that contain thousands of tiny slits per inch
7. Plane mirror
Flat mirrors are called plane mirrors
8. Law of reflection
Angle of incidence = Angle of reflection
9. Snell's Law

10. Regular reflection
11. Diffuse reflection
12. Virtual image (mirror and lens)
If the image is formed by the extension of the rays of light, the image is virtual
13. Real image (mirror and lens)
If the rays of light actually focus at the image, the image is said to be real. A real image can be projected onto a screen.
14. Concave/Convex mirror
15. Concave/Convex lens
16. Principle focus of concave/convex mirror
Halfway between the mirror surface and the mirror's optic center is the focal point. Focal point is important because the reflected rays (or the extension of the reflected rays) that are parallel to the axis will meet at the focal point
17. Focal length
Half of the radius of the sphere of the mirror is the focal length. Focal length is important because mirror equation is based on focal length
18. Principle axis
Principle axis is the line through the center of the mirror and the center of the sphere. Principle axis isn't scientifically important, but it can simplify the drawing of an reflected image.
19. Aberrations
Aberration is caused by differences in refractive index for different wavelengths of light
20. Dispersion of light (also known as "Spectrum")

When white light (which is a combination of all the colors of the visible spectrum) hits a glass prism, the beam is split into its components colors, with Red at the top, then orange, yellow, green, blue and violet at the bottom as red has the highest wavelength while violet has the lowest. This experiment is used to prove that the lower the wavelength the higher the refractive index (i.e refracting more) and you need to visualize the result of the experiment.

Free resources to prepare for SAT II Physics exam

There are very few free resources available on the Internet to help you prepare for SAT II Physics exam. Sparknotes is the only one that we used and would recommend to other students.

The other free resource that most people ignore is Wikipedia.org. Whenever there was something that we didn't quite understand or simply wanted to find out more about something, we looked up on wikipedia. You will be very surprised on how much that process actually can help you understand the topic you are studying.

For example, when we were studying waves, there were a lot of talks on "single slit" on both Princeton Review and Barron's books. We felt a bit lost after reading the text and we looked it up on "wikipedia" and it redirected us to Diffraction. We were surprised at the beginning, but after some thinking, it actually makes a lot of sense.

Then we saw this photo on the wiki page and all of sudden, the text on the books all start to make sense. Reading these black prints on the write paper can becoming really boring, especially when the exam is only weeks away and the pressure is mounting. Study these colorful pictures taken from the Physics lab can really spice things up a little and I'm sure the memory cells last a longer too. On the same page, there is another picture taken from the experiment of "diffraction grating", where it is so bright in the middle.

So whenever you are confused by what these experiment of single slit and double (multiple) slits are trying to prove, just think of these two pictures and it immediately clear things up and it eventually helps you answer some of the questions too.

From next post, I will start sharing some of the study notes we made.