Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 1 Brazil Problem 14 – Circle of Light Brazil Problem 14 Circle of Light Reporter: Felipe de Melo

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 2 Brazil Problem 14 – Circle of Light Problem 14 Circle of Light When a laser beam is aimed at a wire, a circle of light can be observed on a screen perpendicular to the wire. Explain this phenomenon and investigate how it depends on the relevant parameters.

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 3 Brazil Problem 14 – Circle of Light Reflection Refraction Snell’s Law Interference Theoretical Introduction Materials Procedures Data Analysis Experiments Relevant parameters Conclusion

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 4 Brazil Problem 14 – Circle of Light REFLECTION Reflection occurs on the surface of the wire Conic formation

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 5 Brazil Problem 14 – Circle of Light REFLECTION Half of the wire surface All the circle, without the wire shadow Only because the wire is rounded the reflection forms a circle

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 6 Brazil Problem 14 – Circle of Light REFRACTION Refraction occurs through the wire Will form the front part of the circle Higher refraction indeces will distribute the refraction along a bigger part of the circle

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 7 Brazil Problem 14 – Circle of Light REFRACTION Vertical projection plan We will call this angle as beta Both angles are equal

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 8 Brazil Problem 14 – Circle of Light REFRACTION Distance to wire center Incidence angle First angular deviation Refraction angle Wire radius A laser light ray The wire Horizontal projection plan

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 9 Brazil Problem 14 – Circle of Light REFRACTION SNELL’S LAW Best way to quantify both angles is using vectors Incident light ray Refracted light ray Normal straight line in relation with the surface

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 10 Brazil Problem 14 – Circle of Light REFRACTION VECTORIAL FORM OF SNELL’S LAW Refracted light ray unit vector Wire refraction index Air refraction index Normal unit vector Incident light ray unit vector

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 11 Brazil Problem 14 – Circle of Light REFRACTION Inclination in relation to horizontal axis The last refracted ray, with biggest angular deviation

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 12 Brazil Problem 14 – Circle of Light REFRACTION

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 13 Brazil Problem 14 – Circle of Light REFRACTION

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 14 Brazil Problem 14 – Circle of Light REFRACTION Refraction index Light intensity Inclination angle Light intensity Increase the area iluminated by refracted light

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 15 Brazil Problem 14 – Circle of Light REFRACTION Form primaly the front part of the circle

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 16 Brazil Problem 14 – Circle of Light REFRACTION AND REFLECTION Translucid wire Assume absorption equals to zero Energy conservation

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 17 Brazil Problem 14 – Circle of Light REFRACTION AND REFLECTION FRESNEL’S RELATION

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 18 Brazil Problem 14 – Circle of Light REFRACTION AND REFLECTION From spherical geometry: Higher values for beta will increase the reflected light intensity

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 19 Brazil Problem 14 – Circle of Light REFRACTION AND REFLECTION Refraction Reflection

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 20 Brazil Problem 14 – Circle of Light CIRCLE FORMATION Disconsidering the wire dimensions Laser Wire

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 21 Brazil Problem 14 – Circle of Light CIRCLE FORMATION Wire diameter Horizontal inclination Horizontal inclination after refraction Much smaller than other experiment dimensions

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 22 Brazil Problem 14 – Circle of Light INTERFERENCE DOUBLE SLIT PATTERN OF INTERFERENCE Wire diameter Distance between two dark shadows Light wave-length Distance to screen

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 23 Brazil Problem 14 – Circle of Light PREDICTION OF THE RELEVANT PARAMETERS Incident angle The measure of the radius Light intensity distribution Wire dimensions Thinner wires will turn easier to see the interference Refraction Index Light intensity distribution

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 24 Brazil Problem 14 – Circle of Light EXPERIMENTSMATERIALS

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 25 Brazil Problem 14 – Circle of Light EXPERIMENTS CONIC FORMATION Conic formation Height and radius Light intensty Intensity

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 26 Brazil Problem 14 – Circle of Light EXPERIMENTS RELATION BETWEEN HEIGHT AND RADIUS Conic formation Height and radius Light intensty Intensity

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 27 Brazil Problem 14 – Circle of Light EXPERIMENTS LIGHT INTENSITY DISTRIBUTION Point of maximun reflection Point of maximun refraction + Conic formation Height and radius Light intensty Intensity

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 28 Brazil Problem 14 – Circle of Light EXPERIMENTS DIFFERENT SHAPES Laser Screen Wire

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 29 Brazil Problem 14 – Circle of Light EXPERIMENTS DIFFERENT SHAPES

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 30 Brazil Problem 14 – Circle of Light EXPERIMENTSINTERFERENCE Copper wire, only reflects the light

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 31 Brazil Problem 14 – Circle of Light EXPERIMENTSINTERFERENCE Interference + Reflection + Refraction 0.2 mm nylon wire

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 32 Brazil Problem 14 – Circle of Light SUMMARY: THEORETICAL INTRODUCTION

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 33 Brazil Problem 14 – Circle of Light SUMMARY:EXPERIMENTS

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 34 Brazil Problem 14 – Circle of Light CONCLUSIONS RELEVANT PARAMETERS Increase reflectance Laser inclination Refraction Index Define the shape of figure Shape of the wire Position of the surface Visibility of interference Thinner wire diameter

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 35 Brazil Problem 14 – Circle of Light BIBLIOGRAPHY Vector form of Snell’s Law, Available on Access on 20 April REFLECTIVITY; Wikipedia. Available on Access on 10 novemberhttp://en.wikipedia.org/wiki/Reflectivity FRESNEL EQUATIONS; Wikipedia. Available on Access on 10 novemberhttp://en.wikipedia.org/wiki/Fresnel_equations KONG, H. J. ; CHOI, Jin; SHIN, J. S.; YI, S. W.; JEON, B. G.; Hollow conic beam generator using a cylindrical rod and its performances. MV Klein & TE Furtak, Optics, 1986, John Wiley & Sons, New York; Huygens Principle

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 36 Brazil Problem 14 – Circle of Light Thank you!Thank you!

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 37 Brazil Problem 14 – Circle of Light REFRACTION

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 38 Brazil Problem 14 – Circle of Light HEIGHT VARIATION

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 39 Brazil Problem 14 – Circle of Light RADIUS VARIATION (I)

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 40 Brazil Problem 14 – Circle of Light RADIUS VARIATION (II)

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 41 Brazil Problem 14 – Circle of Light RADIUS VARIATION (III)

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 42 Brazil Problem 14 – Circle of Light LIGHT INTENSITY FRESNEL’S EQUATIONS Paralel polarized light Perpendicular polarized light

Team of Brazil Problem ## Title Diego de Moura, Felipe de Melo, Matheus Camacho, Thiago Bergamaschi, Thiago KalifeNakhon Ratchasima, 27 June – 4 July 2015 Reporter: Felipe de Melo 43 Brazil Problem 14 – Circle of Light LIGHT INTENSITY FRESNEL’S EQUATIONS