Materials

Composite materials

Let's take a look at a beam. When you put something on the beam, it'll obviously experience a force of some kind, and will bend. As the beam bends, the particles on the inside of the beam (in this case the inside is the top) will move closer together. This is called compression. The particles on the outside of the beam (in this case the bottom) will move further apart. This is called tension.

Let's have a look at two different materials that we could potentially make our beam out of:

1) Concrete - Concrete has a high compression strength, which means that it fares well in situations where a force is trying to push its particles closer together. As a result, on the inside, where compression is experienced on the beam concrete will not buckle or deform in any way. This is good - we obviously don't want our beam to do this. Unfortunately, concrete does not have such a high tension strength - this means that at the bottom of the beam, where particles are moving away from each other, concrete will crack and fail in this way - this is obviously bad, and we cannot make the beam solely out of this material.

2) Iron - Iron tells the complete opposite story of the one above. Iron has a fantastic tension strength, and when a tensile force is added and tension is experienced, the iron will not crack and fail (within reason, of course). This makes it a fantastic material to use at the bottom of the beam. Iron, however, is not so good with compression. When put under a compression force, iron will tend to buckle and deform. This means that we cannot make the beam out of solely this material, either.

What we do, therefore, is form a composite material - we combine both materials together to form a new material, that adopts the most desirable aspects of both former materials. In this case, where concrete would fail at the underside of the beam when tension is experienced, iron stops the new composite material from cracking and deforming. If we take a look at the inside of the beam, we see that as this area experiences compression - a place where iron would regularly buckle and fail, concrete prevents this from occurring. Therefore, we are able to make a beam that can stand up to both compression and tension.

Lenses and Optics


Curvature of waves

When light is emitted by an object the radiation travels out in a wave like way. It's kind out like the waves seen after a pebble in dropped in a pond. The only difference is that the waves travelling out on the pond are confined to one direction and travel out circularly, whereas the waves given off by an object travel out in shells, in spherical wavefronts. The wave front is what connects wave peaks that are at the same distance away from the source. This is one way of depicting the way in which light travels away from an object. Another way is by drawing a ray. This shows the direction of a single wave, and will always be perpendicular to the wave front, assuming it too originated from the center of curvature. The idea of light travelling in straight lines can be thought of as rectilinear propagation. 

These fronts propagate (or travel) away from the source in the same way as a balloon filling with air. Because the waves propagate from the same source, the object from which they are given off serves as their center of curvature. Curvature  refers to how flat a wave front is. These spherical waves expand as they move away from the source, and therefore their curvature can be thought of  as directly related. The further away from a source a wave front is, the less it's curvature is. In the same way, the closer the wave front is to a source, the higher the value of its curvature. In air, which has a refractive index of 1, curvature of waves can be thought of as:

Curvature = 1 / distance from source

Curvature is therefore inversely proportional to the distance from the source. 

For example, the rays of light leaving a book and travelling 0.4m meters to the eyes (average reading distance) The curvature at the eyes is 1/-0.4 = -2.50 D. As the value of the distance from the source increases, The curvature of the wave tends to zero, therefore, objects infinitely far away will have a curvature of zero, and wavefronts are therefore drawn parallel to each other. 

It is also important to note that converging waves will spread out from a single point, such as the waves delineated above, and converging waves will focus on a single point, having started off being 'spread out'. Cartesian convention states that diverging waves are considered negative, whereas converging waves are generally considered positive. What this means for AS level is the waves before they hit a lens are given a negative value, and the waves after they hit the lens are given a positive value. It's almost like drawing a graph, with the y axis being straight through the lens. anything to the left of this axis will take on a negative value, and anything to the right of the line will take on a positive value. 


Power of waves

The function of a lens is to either increase or decrease the curvature of a wavefront. Lenses have a power, which is simply a measure of how much curvature they add to the wave. The power of a lens is given by the equation:

Power = 1/focal length

The focal length of a wave is the point at which rays to the right of the lens will intersect with one another, if the wavefronts entering the lens are parallel to each other. It is where the light from an object infinitely far away will be focused. 

The wave equation

The wave equation take the power of the lens (how much curvature the lens adds to the wave), and the curvature of the wave entering the lens, and then calculates the curvature of the new wave. From the curvature of the new wave, the point at which the light will be focused can be derived. 

1/v = 1/u + 1/f

Because of cartesian convention, the value for u will be a negative number. 

Drawing ray diagrams 

There are three rules when drawing ray diagrams:

1. A ray parallel to the principle axis when entering the lens will be refracted to the focal point. 
2. A ray going through the centre of the lens will continue; experiencing no change in direction.
3. A ray going through the focal point on its way to the lens will be refracted to be parallel to the principle axis. 

The first image depicts what happens normally, the object is further away from the focal length of the lens. The second image gets a little more confusing. This is what happens when the object is between the focal length and the lens. The waves disperse (due to the three rules above) and when they hit the eye, the brain assumes that the rays have travelled in a straight line on their way to the eye, (it can't really comprehend reflection or refraction) and so creates a virtual image behind the lens, which is where all the rays would meet behind the lens. The third image above is what would happen if the object is on the focal length of the lens, the refracted rays would always be parallel to each other, and so an in focus image would be seen an infinite distance away. 

Materials

Structure and properties

Let's take a close up look at the fibers of a newspaper. We would see that the fibers in this newspaper are long, thin strands that all line up to go in the same direction. This means that if you tear the newspaper one way (vertically in this case), you would face little difficulty. If, however, you were to tear it the other way, you may find it considerably harder to tear in a straight line. This is because when you tear the paper in the first direction, all you're actually doing is separating the fibers. Tear the paper in the other direction, however, and you will find it harder, because you actually have to break the physical fibers of the paper. Imagine the situation as a bunch of pencils, all lined up in a row. Separating them one way is easy just move about half the pencils on way, and the other half the other. That's not an issue. Try and separate the pencils the other way, and you will find it considerable harder - you would actually have to break the pencils in half to move them in this fashion.

A good example of this effect in action is in the making of higher quality paper cups. A company is considering two plastic structures that they can use to make their cups:
A you can see, the molecules in the first cups are arranged in a way similar to newspaper fibers - all in one direction. When you try and tear the cups therefore, it's relatively easy in one direction (separating the molecules) and a lot harder to tear if you're going in the perpendicular direction: 
Let's have a quick look at the structure of the other considered plastic that could be used in this process (below). As you can see, the structure of this plastic is molecules that line up all in the same way vertically, and in the same way horizontally. This means that whichever way you try and tear the cup, you will have to break fibers to do so. This means that the cup is difficult to tear in either direction, is longer lsting and is therefore said to be of a higher quality. 

Materials


Stress and strain

When talking about materials, the two terms above are often used. Stress refers to the amount of force that is being exerted over a particular area. The term breaking stress (often referred to as strength) refers to the amount of stress a material can be subjected to before undergoing a deformation of some kind. 

Stress = Force/Area

Strain, on the other hand, refers to the amount of deformation an object experiences - it is equal to the change in dimension of a deformed object, divided by the dimension of the object before it underwent deformation. Therefore, breaking strain refers to the amount of strain an object can undergo before breaking in some way. 

Strain = Extension/Original length (NO UNITS)

Young's modulus

Young's modulus refers to the amount of stress needed to change a materials shape by a certain amount. It is often written as:

Young modulus = stress/strain (Pa)