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King Saud University Dept of physics and astronomy Final exam – 534 phys First term 19/ 1 / 1429 27/ 1/ 2008 Answer the following questions: 1- A step index fiber has been used to transmit light of wavelength of 0.82 m . This fiber has a core diameter of 50 m and refractive index of 1.48, cladding refractive index of 1.46. If the light coming out from the fiber is expanded to spot with a diameter 2 mm. (a) To focus the light by using a lens, what is the focal length of this lens. (b) If this fiber is used to support only one mode at a wavelength 1250 nm. find the maximum core radius of this fiber. (c) If the fiber is immersed in water (refractive index 1.33). what is the acceptance angle of the fiber. (d) Compute the number of modes propagating in this fiber. (e) Starting from the formula of critical angle sinθc = n2 / n1. Prove that cosθc = ( n12- n22)1/2/ n1 __________________________________________________________________ 2- The total delay time due to both modal distortion and material dispersion is given by 2 mod 2 mat 2 Determine the total delay time in a 1 km fiber for which n1 1.46 , 1% , 2 820nm , 40nm and d n 2 3.2 1010 m1 . d ___________________________________________________________________ 3- If you are given that T ( z , t ) 2 H ( t )1 / 2 K ierfc ( x) 1 / x x 2 / . Show that ( z 2 a 2 )1 / 2 z ierfc ierfc 1/ 2 2( t )1 / 2 2 ( t ) is reduced to 2H (( z 2 a 2 )1 / 2 z ) K Under the assumption that the limit t ____________________________________________________________________ T ( z , ) 4- CO2 laser beam ( 1 kW ) to be focused down to a spot of diameter 0.25 mm on nickel sheet 2.5 mm thick. Find the cutting rate of this laser. L 6.47 106 J Kg 1 ) 8900kgm3 T 3110K ( C = 444 J kg-1K-1 _____________________________________________________________________ 5- A pulsed Nd:YAG laser beam used in eye surgery emits a pulse of energy of about 1 mJ in 1 ns. The laser beam is focused to a tiny spot of 30 m diameter in the interior of the eye. ( a ) What is the power density of the laser beam at the focal spot. (b) Assuming that the electric field strength of the laser beam at any point is given by 2 Ee 1 n c E0 2 Where, E e is the power density, is the permittivity of the eye medium, n is the refractive index, c speed of light, E0 is the electric field strength. If n = 1.33 for eye and 78 0 where 0 is the vacuum permittivity and equal to 8.854X 10-12 C2/ Nm2. Find the electric field strength at the focal spot in the eye. ____________________________________________________________ 6- Laser Doppler Velocimetry technique ( LDV) is used to measure the speed of objects. Suppose a HeNe laser ( 632.8 nm) beam is reflected from a traveling car and the recorded shift in the frequency of the laser beam is 6.32 x 107 Hz. Find the speed of the car. ____________________________________________________________________ 7- Discuss the effects which result from the interaction of laser radiation with issues. ____________________________________________________________________ حممد بن صاحل الصاحلي.د أمتىن للجميع التوفيق