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Unformatted text preview: Total internal reflection Reflection and Refraction 4.2 Total internal reflection Dispersion Rainbows • In total internal reflection all of the light is reflected at the interface between two media. • Total internal reflection occurs when the angle o of refraction is equal to or greater than 90 • Total internal reflection is important for optical communications. (light pipe) Total internal reflection Total Internal Reflection Total Interna l ref lec tion Critical Angle θ c n si nθ = n si n(90o ) =n 1 c 2 2 n must be les s tha n n 2 1 Critical Angle At the critical angle
n 2 n =1.00 2 Question W hat is the critical angle at the air water interface? sin c = q
n < n 2 1 n 2 n1 θc n 1 n1 =1.333 qc W hen θ > θ , light is totally internally refl ected c sin qc = n 1.00 2 = = 0.750 n1 1.333 qc = 48.6o 1 The fishes’ eye view of the outside world is lim ited by total internal reflection Optical Fiber Light Pipe An optical fiber (light pipe) confines the light inside the m aterial by tot al internal refl ection. If the refractive index of the fiber is 1.52 what is the sm allest angle of incidence possibl e when the light pipe is in air. q2 = 90 q1 n =1.00 2 n =1.52 1 n1 sin q1 = n2 sin q2 sin q1 =
At a ngles greater than the critical a ngle the wha le sees only ref lec te d li ght This i llustrates the poi nt that the pat h of li ght rays is the sa me i n the forward and reverse directions. n2 sin 90 (1.0 )(1.0 ) = = 0 .66 n1 1.52 q1 = 4 1o Fiber Optics Fiber optics are used ext ensi vely in comm unications. Tel ephone, Internet, The high frequency of light (com pared to microwaves) all ows it to be switched rapidly and carry m ore inform ation. Light Pipe A light pipe is a flexible fiber that confines a beam of light by total internal reflection Fiber Optic are used in optical comm unication networks Diamond cut The advant age of optical comm unication syst em s is due to the higher frequency of light 1 f~10 5 Hz com pared to radio or microwaves 8 f~10 1010 Hz For a we ll cut dia mo nd the i ncide nt li ght is tota lly i nterna lly ref lec ted. The hi gh refrac tive inde x of the dia mond allo ws tota l i nterna l ref lec tio n over a wi de range of angles . 2 Dispersion • The index of refraction generally is different for different wavelengths of light. • This dispersion can be used to separate light into different wavelengths using a prism. • Dispersion is a problem in fabricating lenses for imaging – causing chromatic aberration, different images for different wavelengths of light • Dispersion is responsible for rainbows. Dispersion of white light by a prism Separation of different wa ve lengths by ref raction through a Prism Inci dent W hite Light The index of refraction varies with wavelength exam ple for Crown Glass vio let 400 1.538 green 500 1.526 red 700 1 .516 max i mum cha nge vio letred Example 35.6 A prism disperses white light into different colors. A 90 degree prism of crown glass refracts light normally incident on the long surface.. Find the largest difference in angles of refraction of violet and red light for different values of q. θ =q 1 q n=1.0000 n1 sin q1 = n sin 2 q sin 2 = q n 1 sin q n θ 2 θ 1 n1 vio let n = 1 .538 1 red n = 1.516 1 vio let li ght is ref racted more than red Dn » 1 .4 % n qviolet - qred = a rc sin(nviolet sin q) - a rc sin(nred sin q) Prism max difference when o q2 > 90 for violet q=40.556
θ 1 n 1
de l ta t het a ( deg r e e s) Rainbow Dq plotted vs q2 1 0 9 8 7 6 5 4 3 2 1 0 0 2 0 4 0 6 0 8 0 1 0 0 n=1.0000 Th e t a vi o l e t (de g r e e s ) Dθ
90o Dq ~9.5 degrees o at q=40.556 sinq q The large difference is bec ause near 90o (Maxim um ) sin q is quite insensitive to q A rainbow is seen on a rainy day when the sun is to your back, o low in the horizon (l ess than 42 above the horizon) A second rainbow is often seen with the order of col ors reversed. 3 The shape of the rainbow is due to parallel beam of sunlight light refl ected and refracted from raindrops at a special angl e (rainbow angl e 42o ) The col ors of the rainbow are due to dispersi on of the light. The raindrop reflects and refracts the incident sunlight. Incident beam is refracted twice and internally reflected by the raindrop Deflection angle = 180j Rainbow angle Incident light is refl ected at m any different angl es How ever m uch of the light is refl ected near the rainbow angl e 42o bec ause j vs θ goes through a m axim um 45 40 35 P h i ( d e g r e e s ) Effect of dispersion j n
larger n => sm aller j Blue light has sm aller j Blue light is on the inside of the arc Red light is on the outside 30 25 20 15 10 5 0 0 20 40 60 80 100 th e ta (d e g r e e s) Near the m axim um there are a large num ber of values of θ with the values close to jmax Colors of the rainbow The pri mary rainbo w has blue o n the insi de a nd red o n the outside The sec ondary rai nbo w is due to li ght tha t is i nterna lly ref lec ted twice the effec t of refraction is to i ncrease j and the colors are reversed (see proble m 60). 4 ...
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