Lecture Videos

• Light behaves as a particle (photon) when it is emitted or absorbed but it travels through space as an electromagnetic wave
• Light travels as rays
• Three interactions of light:

  • reflection
  • transmission
  • absorption
• Absorption: light -> heat

  Transmission: light goes through

  Reflection: light bounces
• Law of Reflection: incident angle is equal to the angle of reflection
• Fermat's Principle of Least Time:

  • light takes the shortest path in time
  • light takes the fastest path
• Two types of reflection: specular and diffuse
• Diffuse reflections let you see the reflector. The reflector as the object doing the reflecting
• Specular refections let you see the light source
• Mirrors are perfect specular reflectors
• Plane mirror is flat
• Curved Mirrors are either convex where shiny is outside and concave is where shiny is inside
• LIGHT INTERACTIONS

  When light moves from one place to another, we treat it as if it is moving in a straight line until it hits something. This method is called the ray model of light. When light interacts with anything- a rock, a piece of glass, the atmosphere of earth, water in a cup, etc, it will do three things. 
• LIGHT INTERACTIONS

  • reflect - Light bounces off of the surface according to the law of reflection.
  • transmit - Light passes through the material.
  • absorb - Light will be absorbed by material, often turning in to thermal energy.
• LAW OF REFLECTION

  When light bounces off of a surface it follows a very simple law: the law of reflection. This law states that the incident angle is equal to the angle of reflection. This angle is measured from "the normal" meaning that these angles are measured from a line perpendicular to the surface that they are bouncing off of.
• TYPES OF REFLECTION

  There are two primary "types" of reflection. Specular reflection is the type of reflection you see in a mirror, and it lets you see the object that light is coming from before the reflection. Diffuse reflection is reflection that spreads light out in all directions as it hits the surface. This reflection is what allows us to see things that aren't shiny- you can see a tree because of light reflecting in all directions off of it. Diffuse reflection lets you see the object that is doing the reflecting.
• Mirrors are typically human made surfaces that are very smooth and thus are excellent at specular reflection. The three main types of mirror are plane (flat) mirrors, convex (curved, outside shiny) mirrors, and concave (curved, inside shiny) mirrors.
• Plane mirrors are fairly straight forward- they follow the law of reflection and the image of whatever object is reflected in the mirror is the same size and distance from the mirror.
• Curved mirrors are a little more deceptive. They still obey the law of reflection and nothing else, but the curve of the mirror makes some strange effects happen- often making the image larger or smaller, and giving the object a larger or lesser range to be in while still reflecting completely.
• FERMAT'S PRINCIPLE OF LEAST TIME AND REFRACTION

  We actually used this idea- that light will take the path that takes the least amount of time- to justify the law of reflection in our zoom lecture. Now we will use it to describe the transmission of light through a medium. So far, in all of our discussion of light, we've stated that light moves at a constant speed of roughly 300,000,000 m/s. This "top speed" of light of "c" only happens in empty space, but when travelling through matter the EM waves slow down jiggling charges around.
• FERMAT'S PRINCIPLE OF LEAST TIME AND REFRACTION

  While light moves at almost "c" in our atmosphere (it moves at 0.9997c) it tends to slow down considerably in other materials like glass (vlight=0.67c), and even slower materials like diamond (vlight=0.42c). Fermat's principle comes in when light moves from one material such as air to another material like glass. When this happens, the light slows down considerably. Fermat's principle still holds true though- light will always take the fastest path.
• FERMAT'S PRINCIPLE OF LEAST TIME AND REFRACTION

  When light is forced through a path that involves different speeds, it will bend at the interface between the two materials. It will bend such that the path it takes is the shortest path in terms of time- this usually amounts to the light travelling a longer distance in a fast material (like air) and bending to travel less distance in a slow material (like glass). The bending of light due to the combination of different speeds in different materials and Fermat's principle is called refraction.
• SAMPLE RAY DIAGRAMS

  Check out some of these ray diagrams showing light bend as it hits the surface between air and glass. Notice in this first one how light does not bend when it hits perpendicular to the surface. This is because going straight from the surface to point B is already the shortest possible path that light can take in the slow material (glass). The path from A to C does bend however- it bends such that the light goes from A to the surface  taking a longer path in the fast material, but it bends going from the surface to point C taking a shorter path in the slow material.
• SAMPLE RAY DIAGRAMS

  In the following ray diagram light You see light travelling from point A to point B directly across the prism. The fastest path is not going straight across though! Instead the ray goes up a bit to take a shorter path across the prism before turning back down to B. Going from A to C shows the familiar trait of light of spending as little time in a slow material as possible.
• WHY DOES THIS HAPPEN

  Refraction occurs due to the wave-nature of light. It is the first of many wave phenomena that we will study with light. Light haves are EM waves, with both electric and magnetic fields oscillating at the wave's frequency. As the wave crashes in to a barrier between two different materials the frequency does not change- but the speed does. Since v=fλ, if the frequency f is held constant, then the only way to slow the EM wave down is for the wavelength (λ) to be shorter.
• WHY DOES THIS HAPPEN

  This is equivalent in the "walking" analogy of speed, frequency, and wavelength to walking on dry land, but then crossing a puddle. You might continue to take steps at the same rate, but as you hit the puddle your steps become shorter as it is more work to drag your foot through the mud. While you are taking the same number of steps each minute- you still slow down due to taking shorter steps.
• WHY DOES THIS HAPPEN

  The following gif shows the wave fronts crashing in to the barrier between two media. The peaks (in white) and troughs (in black) hit the surface where they move slower. If you pick a peak and follow it as it hits the surface, you'll notice that it moves slower in the second material. Because it moves slower it literally has less time to get away from surface before another peak hits. This slowdown results in light bending, simply because a peak remains a peak (or a trough remains a trough) as it hits the surface and slows down.
• INDEX OF REFRACTION

  Materials that allow light to transmit through themselves also slow the light down. We can characterize these materials with a single number, the index of refraction, that tells us how much light slows down. The index of refraction is defined as n=cv where n is the index of refraction (unitless), c is of course the speed of light in a vacuum, and v is the speed of light inside that material.
• INDEX OF REFRACTION

  Water, for example, has an index of refraction of 1.33. This means that 1.33=cv can be rearranged to find the velocity of light in water v=c1.33=0.75c or light in water travels at 75% the speed of light in a vacuum.
• INDEX OF REFRACTION

  The more light slows in a material, the more it will bend. This is manifested in "Snell's Law."
• SNELL'S LAW

  Given light from material 1 is crossing a boundary in to material 2 at an angle of θ1, it will enter material 2 at an angle of θ2 according to Snell's Law: n1sin⁡(θ1)=n2sin⁡(θ2). Following is a diagram showing where each of these quantities are.
• SNELL'S LAW

  Notice how from 0 to 90 degrees the sine function just increases- the rate that it is increasing varies, but it only goes up (and levels off exactly at 90). Also, imagine a reflecting ray, the angle of incidence can only go from 0 to 90 degrees. 
• SNELL'S LAW

  This means that if the indices of refraction (n1 and n2) are held constant, we can make some relationships appear:

  • If n1=n2 then θ1=θ2
  • If n1<n2 then θ1>θ2
  • If n1>n2 then θ1<θ2
• SNELL'S LAW

  In other words: if the index of refraction increases as light crosses a boundary, it bends towards the normal line. If the index of refraction decreases as light cross a boundary, light bends away from the normal line.