Optics

Optics is an event for divisions B and C during the 2010/11 season. This event deals with geometric and physical optics, such as reflection, refraction, critical angle, electromagnetic and visible spectrum, lenses, and mirrors. Competitors for this event may bring any type of calculator and should have knowledge of SI units, as all answers will require a student to know and understand them. Some aspects of optics are similar to the former event Crave the Wave, though optics focuses on light while Crave the Wave was about waves in general.

Introduction to optics
Optics is a science which studies light. Optics is usually divided into two 'subfields': geometric and physical optics. Geometric optics studies how light travels, and includes concepts of reflection and refraction. In geometric optics, light is thought of as rays which travel in a straight line (for the most part; I'll talk about refraction later).

Physical optics studies the nature of light, as well as phenomena which cannot be explained by the ray approximation used in geometric optics. Physical optics includes the visible and electromagnetic spectrum, and concepts such as interference.

Geometric Optics
When waves of light (or electromagnetic waves in general) hit the boundary between two mediums, there are several ways that the light can react. Namely, it can reflect, refract, or be absorbed into the second medium. These will be explained below.

Reflection
The law of reflection states:


 * The angle of incidence of a wave or stream of particles reflecting from a boundary, conventionally measured from the normal to the interface, is equal to the angle of reflection, measured from the same interface.

This may seem very complicated, but it really isn't that hard to understand. For reflection to occur, you need a "wave or stream of particles" and an interface. Light, of course, takes the former role. For our purposes, let's assume that the interface is a mirror.

Figure 1 is a convenient example of reflection. In the diagram, PO is an incoming ray of light about to reflect off a mirror. OQ is the ray after it has hit the mirror. You also can see a new line, called the "normal". This is an imaginary line through point O, which is perpendicular to the mirror. The angle of incidence is the angle labeled θi, and the angle of reflection is the one labeled θr.

From this, we can represent the law of reflection by the following simple equation: θi = θr

You can also conclude that the complimentary angles to θi and θr will be congruent.

Refraction
The speed of light is always constant when in a vacuum. However, light can change speeds while traveling through different mediums, such as air, water, and glass. The optical density of a medium measures how well it can transmit light. Water has a higher optical density than air, so light travels slower in water than it does in air. Note that optical density is different than the actual density of a medium.

Another way to characterize the refraction of light between media is with the index of refraction, which is useful in determining the angle at which light refracts at a boundary. The index of refraction is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium. When light strikes a boundary between media at an angle, the refractive index can be calculated by using $$n = \frac{\sin a_1}{\sin a_2}$$ where $$a_1$$ is the angle the light is traveling at in the first medium relative to the normal, and $$a_2$$ is the angle the light is at after it passes through the second medium relative to the normal. By dividing the sines of those two angles, you have the index of refraction. This equation is known as Snell's law and can also be used backwards to find the angle at which light leaves if you know both the index of refraction of the second medium and the angle at which the light entered. The refractive index of a medium is constant for every angle at which light can enter, but it is different for every wavelength of light. This is why light disperses in a prism.

Sample Questions
Example Station 1: Measure the focal length of convex and/or concave lenses and/or mirrors

Example Station 2: Using ray-tracing techniques, find the image/object locations of one and/or two lens and/or mirror systems. Specify the image/object characteristics (real/virtual, magnification, erect/inverted, object/image distances, lens/mirror focal lengths).

Example Station 3: Set up mirrors and/or lenses to direct a beam of light on to a target around an obstacle. The object is to have the student set up the problem, but the supervisor turns on a light such as a Maglite (or laser). For the first year prisms are not to be used!

Example Station 4: The object is to align a beam from a light source provided by the officials to bounce off all given mirrors (Division C only may also include lenses and refraction) to strike a given target. Students will begin with a set number of points and then points will be deducted for the time it takes to set up the devices and the distance that the light ends up from the center point of the target.