Lecture Outline. Scattering at an Interface Sunrises & Sunsets Rainbows Polarized Sunglasses 8/9/2018. EE 4347 Applied Electromagnetics.

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Course Instructor Dr. Raymond C. Rumpf Office: A 337 Phone: (915) 747 6958 E Mail: rcrumpf@utep.

1 Course Instructor Dr. Raymond C. Rumpf Office: A 337 Phone: (915) E Mail: rcrumpf@utep.edu EE 4347 Applied Electromagnetics Topic 3i Scattering at an Interface: Examples Examples These notes may contain copyrighted material obtained under fair use rules. Distribution of these materials is strictly prohibited Slide 1 Lecture Outline Scattering at an Interface Sunrises & Sunsets Rainbows Polarized Sunglasses Examples Slide 1

2 Scattering at an Interface Examples Slide 3 Numerical Example (1 of 11) Determine the following: 1. The critical angle c for both and polarizations. The Brewster s angle B for both and polarizations 3. Angle of transmission t of both and polarizations 4. Impedance of both media 1 and 5. Reflection coefficient r for both and polarizations. 6. Transmission coefficient t for both and polarizations. 7. Overall reflectance R of the wave 8. Overall transmittance T of the wave 9. Does R + T = 100%? If not, why not? 10. Polarization of the reflected wave. Examples Slide 4

3 Numerical Example ( of 11) 1 The critical angle c for both and polarizations The critical angle c is the same for both polarizations. 1 n c sin n1 n n1 There is no critical angle because this example has n 1 < n. Aside: there is a critical angle for waves propagating from water to air c sin Examples Slide 5 Numerical Example (3 of 11) The Brewster s angle B for both and polarizations Assuming there is no magnetic response, we only have a Brewster s angle for the polarization component of the wave. n tanb, n1 1 n B, tan n tan 1.0 B, 53 Examples Slide 6 3

4 Numerical Example (4 of 11) 3 Angle of transmission t of both and polarizations Both polarizations will have the same angle of transmission. It is calculated using Snell s law. n sin n sin 1 i t n 1 1 t sin sini n sin sin t 37 Examples Slide 7 Numerical Example (5 of 11) 4 Impedance of both media 1 and Assuming no magnetic response, r,1 r, 1 Therefore, the impedances are 1 0 n 1 0 n Examples Slide 8 4

5 Numerical Example (6 of 11) 5 Reflection coefficient r for both and polarizations. r cosi 1cost cos cos r i 1 t cos cos cos cos 37 r cost 1cosi cos cos t 1 i 6 r cos cos cos cos 53 Examples Slide 9 Numerical Example (7 of 11) 6 Transmission coefficient t for both and polarizations. t 1r t r t cost t cos i i 1r cos cos 1 0 cos53 cos37 t t Examples Slide 10 5

6 Numerical Example (8 of 11) 7 Overall reflectance R of the wave The reflectance for both polarizations separately are R r R R r 0 R 0 The applied wave is circularly polarized so both and have equal power in them. Therefore, the overall reflectance is 50% 50% 50% % 0 R R R R Examples Slide 11 Numerical Example (9 of 11) 8 Overall transmittance T of the wave The transmittance for both polarizations separately are T T t t cos cos cos53 1 t cos i cos cos cos53 1 t cos i T T 1.00 The applied wave is circularly polarized so both and have equal power in them. Therefore, the overall transmittance is 50% 50% 50% % 1.00 T T T T Examples Slide 1 6

7 Numerical Example (10 of 11) 9 Does R + T = 100%? If not, why not? RT Yes! This power is conserved. Examples Slide 13 Numerical Example (11 of 11) 10 Polarization of the reflected wave. The wave is incident at the Brewster s angle where the polarization is completely transmitted. This means it is only the wave that gets partially reflected. The reflected wave can only be polarized. Examples Slide 14 7

$Sunrises & Sunsets Examples Slide 15 Sunsets and Equinox horizon Observed position of sun. Actual position of sun. Light rays curve due to refraction through the atmosphere. El Paso, TX 31.$ $Due to refraction, this is not true. The equinox for El Paso, TX occurs on September, 01. In reality, we will have equal day and night on September 6 if we account for refraction.$

8 Sunrises & Sunsets Examples Slide 15 Sunsets and Equinox horizon Observed position of sun. Actual position of sun. Light rays curve due to refraction through the atmosphere. El Paso, TX N, W Equinox At the equinox, the earth s tilt is neither away or toward the sun. We commonly think then that day and night are of equal duration. Due to refraction, this is not true. The equinox for El Paso, TX occurs on September, 01. In reality, we will have equal day and night on September 6 if we account for refraction. Sept duration of day 1h, 7m, 18s (accounting for refraction) Sept 6 duration of day 11h, 59m, 36s (accounting for refraction) We conclude that days are just over 7 minutes longer than would be without refraction. Examples Slide 16 8

9 Rainbows Examples Slide 17 Rainbows (1 of ) There is actually a lot of physics involved with rainbows. There are always multiple rainbows. Very often they are just too dim to see. Examples Slide 18 9

$. Dispersion The refractive index of water is slightly different for each color of light, so the angle of light$

10 Rainbows ( of ) Rainbows form due to: 1. Total Internal Reflection Light reflects twice inside of a raindrop and exits at around 41 away from the incident light.. Dispersion The refractive index of water is slightly different for each color of light, so the angle of light leaving the raindrop is different for different colors. Thus, the colors spread apart as the sun light propagates away from the raindrop. Examples Slide 19 Polarized Sunglasses Examples Slide 0 10

Polarized Sunglasses (1 of ) Polarized sunglasses reduce glare (i.e. reflections from surfaces) Without polarized sunglasses With polarized sunglasses Light tends to become partially polarized upon reflection from water, glass, and most manmade objects.

11 Polarized Sunglasses (1 of ) Polarized sunglasses reduce glare (i.e. reflections from surfaces) Without polarized sunglasses With polarized sunglasses Light tends to become partially polarized upon reflection from water, glass, and most manmade objects. Polarized sunglasses block this polarization allowing you to see the surface and what is behind it instead of the reflected light. Some glare remains because the reflected light is only partially polarized. Examples Slide 1 Polarized Sunglasses ( of ) Consider Fresnel reflection from air to water. The polarization is more strongly reflected, thus polarized sunglasses block this polarization. Examples Slide 11

Lecture Outline. Scattering at an Impedance Discontinuity Power on a Transmission Line Voltage Standing Wave Ratio (VSWR) 8/10/2018

Lecture Outline. Scattering at an Impedance Discontinuity Power on a Transmission Line Voltage Standing Wave Ratio (VSWR) 8/10/2018 Course Instructor Dr. Raymond C. Rumpf Office: A 337 Phone: (95) 747 6958 E Mail: rcrumpf@utep.edu EE 4347 Applied Electromagnetics Topic 4d Scattering on a Transmission Line Scattering These on a notes