Applications of Prisms and Math :: Mathematics

Missing FiguresPrisms and their ApplicationsIntroductionA prism is bingle or several blocks of glass, through and through which infirm passes and refracts and reflects make its straight surfaces. Prisms ar used in two fundamentally varied ways. One is ever-changing the orientation, fixing, etc. of an image or its parts, and another is dispersing turn on as in a refractometers and spectrographic equipment. This project will yet(prenominal) deal with the branch use.Consider an image projected onto a natural covering with parallel rays of light, as opposed to an image formed by the similar rays that are passed through a cubic prism (assume that the amount of light that is reflected is negligible). The rays that pass through the prism will not be refracted since the weight down of refraction = sin-1(sin(0)/n) = 0, or reflected, so the images will be exactly the alike(p). more generally, if the rays enter and abjure a prism at right angles (Assuming the rays solely travel s through star medium while passing through the prism), the only effect on the image will be the reprimand of the rays off-key of its surfaces. Since the law of reflection I= -I (Angle of incidence equals the negative of the angle of reflection) is not effected by the medium, the effect of the prism will be same as that of pondering surfaces or mirrors placed in the same location as the brooding surfaces of the prism. It follows that to understand prisms it is important to understand how mirrors post be used to alter the direction of rays.Mirror LocationProblem 1Consider the by-line exampleA horizontal ray is demand to undergo a 45-angle change and this has to be achieved using a mirror. We need to go up how the mirror should be oriented to achieve the want change of angle. final resultRecall the Snells law which deals with refractionsinI0 /n0 = sinI1/n1if we dress the incoming and outdo rays ray and the normal of the refractive surface as vectors and using a property o f the cross-product we can say the followingQ0xM1 = Q0M1 sinI0 = sinI0and in like mannerQ1xM1 = Q1M1 sinI1 = sinI1thusN0 (Q0xM1)= n1 (Q1xM1)If we enroll two new vectors S0 and S1 and let them equal n0 Q0 and n1Q1 respectively we will postureS0x M1 = S1xM1or(S1-S0)xM1 = 0this implies that (S1-S0) are parallel or anti-parallel, which means that we can define a new variable which is called the astigmatic constant withS1 S0 = M1How is reclaimable for solving our problem?Applications of Prisms and Math MathematicsMissing FiguresPrisms and their ApplicationsIntroductionA prism is one or several blocks of glass, through which light passes and refracts and reflects off its straight surfaces. Prisms are used in two fundamentally different ways. One is changing the orientation, location, etc. of an image or its parts, and another is dispersing light as in a refractometers and spectrographic equipment. This project will only deal with the first use.Consider an image projected onto a screen with parallel rays of light, as opposed to an image formed by the same rays that are passed through a cubic prism (assume that the amount of light that is reflected is negligible). The rays that pass through the prism will not be refracted since the angle of refraction = sin-1(sin(0)/n) = 0, or reflected, so the images will be exactly the same. More generally, if the rays enter and leave a prism at right angles (Assuming the rays only travels through one medium while passing through the prism), the only effect on the image will be the reflection of the rays off of its surfaces. Since the law of reflection I= -I (Angle of incidence equals the negative of the angle of reflection) is not effected by the medium, the effect of the prism will be same as that of reflective surfaces or mirrors placed in the same location as the reflective surfaces of the prism. It follows that to understand prisms it is important to understand how mirrors can be used to change the direction of rays.M irror LocationProblem 1Consider the following exampleA horizontal ray is required to undergo a 45-angle change and this has to be achieved using a mirror. We need to find how the mirror should be oriented to achieve the desired change of angle.SolutionRecall the Snells law which deals with refractionsinI0 /n0 = sinI1/n1if we define the incoming and outgoing rays ray and the normal of the refractive surface as vectors and using a property of the cross-product we can say the followingQ0xM1 = Q0M1 sinI0 = sinI0and alsoQ1xM1 = Q1M1 sinI1 = sinI1thusN0 (Q0xM1)= n1 (Q1xM1)If we introduce two new vectors S0 and S1 and let them equal n0 Q0 and n1Q1 respectively we will getS0x M1 = S1xM1or(S1-S0)xM1 = 0this implies that (S1-S0) are parallel or anti-parallel, which means that we can define a new variable which is called the astigmatic constant withS1 S0 = M1How is useful for solving our problem?