N = e r 1/2 becomes troublesome if e < 0, which, as we know, is perfectly possible. Change the arrow directions in the picture above (or in all other pictures likeĪ not-so-nice thing might be that the definition of Obviously, all we need to know for this is the frequency dependence of theĭielectric constant e( n), something we have treated extensively before.Ī nice thing in geometric optics is that the direction of the light paths is always reversible. n = n( n) so we can construct light paths for the various frequencies (= colors) of visible light. Going a bit beyond that, we would also like Through optical devices like lenses or prisms. It already possible to construct light paths or light rays running Knowing only the index of refraction n makes Propagation c inside materials, frequency n and wavelength l in materials or in vacuum, is Know about Snellius law and some other basic optics parameters like the speed of The decisive material quantity in geometric optics (and beyond) is the index of refraction together with Snellius law. A light beam going through an optical grid is diffracted. " bending" of light beams around corners and all the other effects bringing aboutĭirectional changes and interference effects. " bending" or "flexing" of light beams at the interface between two different Reflection is, well, reflection always with (or dispersing or diverging) lenses allow to manipulate the light path, e.g. Convex (or collecting or converging) lenses and concave Have an index of refraction n > 1, and light hitting a transparent Optically transparent materials ("glass") The essence of basic high-school geometric optics is shown in the following pictures: In other words, you really need to understand the ideas on this page before you can move on to any other area of geometry.5.1.2 Basic Geometric Optics 5.1.2 Basic Geometric Optics Planes are important because two-dimensional shapes have only one plane three-dimensional ones have two or more. Shapes, whether two-dimensional or three-dimensional, consist of lines which connect up points. Angles are formed between two lines starting from a shared point. Points, lines and planes underpin almost every other concept in geometry. If you want to write the measured angle at point B in shorthand then you would use: ∠ABC is the same as ∠CBA, and both describe the vertex B in this example. The middle letter in such expressions is always the vertex of the angle you are describing - the order of the sides is not important. The expression ∠ABC is shorthand to describe the angle between points A and C at point B. The angle symbol ‘∠’ is used as a shorthand symbol in geometry when describing an angle. This may seem unimportant, but it is crucial in some complex situations to avoid confusion. Our shape can be described ‘ABCDE’, but it would be incorrect to label the vertices so that the shape was ‘ADBEC’ for example. In a closed shape, such as in our example, mathematical convention states that the letters must always be in order in a clockwise or counter-clockwise direction. The plural of vertex is vertices. In the example there are five vertices labelled A, B, C, D and E. Naming vertices with letters is common in geometry. Tick marks (shown in orange) indicate sides of a shape that have equal length (sides of a shape that are congruent or that match). The single lines show that the two vertical lines are the same length while the double lines show that the two diagonal lines are the same length. The bottom, horizontal, line in this example is a different length to the other 4 lines and therefore not marked. Tick marks can also be called ‘ hatch marks’.Ī vertex is the point where lines meet (lines are also referred to as rays or edges). See our page on Angles for more information. The shape illustrated here is an irregular pentagon, a five-sided polygon with different internal angles and line lengths (see our page on Polygons for more about these shapes).ĭegrees ° are a measure of rotation, and define the size of the angle between two sides.Īngles are commonly marked in geometry using a segment of a circle (an arc), unless they are a right angle when they are ‘squared off’. Angle marks are indicated in green in the example here.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |