SJSU EE 140 - soln140_MT2a_S15 (3 pages)

EE140 Mid Term 2 Dr Ray Kwok Student Name Last First 1 35pts Glass isosceles triangular prisms shown in Figure are used in optical instruments Assuming r 4 for glass calculate the normally incident light power reflected back in dB by the prism as shown if the light is unpolarized At the first water glass interface nglass 4 2 n1 n2 1 2 1 n1 n2 1 2 3 Inside of the prism nglass sin c nair sin 90o sin c P 1 2 c 30o total reflection for both polarizations At the last glass water interface 2 2 1 1 2 1 3 Total power coming back at the bottom is 2 1 P 1 1 1 2 1 0 79 79 1 02 dB 9 Note The polarization here doesn t do anything since both polarizations have the same reflection transmission properties 2 2 EE140 Mid Term 2 Dr Ray Kwok r 2 35 pts A plane wave in air with H x 2 sin t 3 y 4 z mA m is incident upon the planar surface of a dielectric material with n 1 5 occupying the half space z 0 Write the full expression for the reflected E field and the transmitted H field n1 r k i 4 z 3 y n2 Er Hr transmission t O r i Ei ki kr k1 32 4 2 5 Et reflection ck1 1 5 10 9 kt Ht z 3 4 n1 sin i n2 sin t tan i y incidence 3 1 1 5 sin t 5 t 23 6 o Hi n1 cos t n2 cos i 1 cos 23 6 o 1 5 4 5 0 134 n1 cos t n2 cos i 1 cos 23 6 o 1 5 4 5 r Er z sin r y cos r o H oi sin t k1 y sin r z cos r r Er z 3 5 y 4 5 0 134 377 0 002 sin t 5 y 3 5 z 4 5 r Er z 0 06 y 0 08 sin 1 5 10 9 t 3 y 4 z V m 2 n1 cos i 2 1 4 5 0 76 n1 cos t n2 cos i 1 cos 23 6 o 1 5 4 5 k 2 k o n2 5 1 5 7 5 r H H t x o oi sin t 7 5 y sin t z cos t 2 r H t x 0 76 1 5 2 sin t 7 5 y sin 23 6 o z cos 23 6 o r H t x 2 27 sin 1 5 10 9 t 3 y 6 87 z mA m EE140 3 Mid Term 2 Dr Ray Kwok 30 pts It is extremely difficult to recover an underwater Black Box by air Assuming the Box is emitting a 100W RHCP 10 kHz signal from the bottom of the ocean 8 km deep estimate the power intensity reaching a helicopter 100 m above the surface Use r 81 r 1 4 S m for seawater The following steps would guide you through your estimation a What is the max power intensity reaching the surface from below if water is lossless assume isotropic radiation b With the attenuation of sea water what is the power intensity right underneath the surface c What is the critical angle Remember this is a lossy medium d Estimate the total power reaching the surface within this critical cone The cone is defined by rotating the critical angle about the normal e What is the fractional power being reflected at normal incident f Assume the reflection coefficient is uniform does not depends on incident angle how much total power is being transmitted g What is the max power intensity reaching a helicopter flying by at 100 m above water a S 100W 4 80002 1 24 x 10 7 W m2 4 b tan 8 9 10 4 2 10 4 81 10 9 36 Good conductor z 2 10 4 4 10 7 4 0 40 2 2 e 2 r e 2 0 40 8000 3 3 10 2780 27800dB W S 1 24 10 7 3 3 10 2780 4 1 10 2787 2 m y c k1 0 40 d For this small angle one can estimate the power within the critical angle is P S R C S 8000 5 3 10 4 2 2 3 10 2785 W 2 e 2 1 j 0 4 1 j 1 j 0 1 0 141 45o 4 2 1 377 1 j 0 1 0 9995 0 03o 2 1 377 1 j 0 1 2 0 9989 99 89 f 0 11 transmitted 2 5 10 2788 W g Power intensity 2 5 10 2788 W 4 1002 2 10 2793 W m2 2 104 2 1 10 4 c 3 108 k1 sin 1 k 2 sin 2 k2 0 4 sin C 2 1 10 4 sin 90o C 0 03o 5 3 10 4 radians