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6. [0/1 Points] PREVIOUS ANSWERS WAUNIPHYSAV1 35.P.018.TUTORIAL. ASK YOUR TEACHER PRACTICE ANOTHER Light of wavelength i. = 632.8 nm from a He-Ne Laser illuminates a pair of identical slits a distance d = 0.230 mm apart, forming an interference pattern on a screen a distance L = 2.90 m away. For the point P a distance y = 4.55 cm from the midpoint of the central maximum, determine the following. (a) Its location in the interference pattern by giving the maximum and minimum between which it is located (Give your answer in integer values.) Between the m = x Can you write an expression for the condition for constructive interference? Can you write an expression for the condition for destructive interference? For small angles, how does sin 9 compare to tan 9? minimum and the m = |:] x Can you write an expression for the condition for constructive interference? Can you write an expression for the condition for destructive interference? For small angles, how does sin 9 compare to tan 9? maximum (b) The ratio of the intensity 1,, at the point P to the intensity Icen at the midpoint of the central maximum Lx ICEn How is the intensity of the interference pattern at the point P related to the intensity at the midpoint of the central maximum and the phase difference q; for the light from the two slits? Can you express the phase difference for the light arriving at the point P from the two slits in terms of the distance to the point P from the central maximum and other known quantities? Q Tutorial 7. [0/1 Points] PREVIOUS ANSWERS WAUNIPHYSAV1 35.P.020. ASK YOUR TEACHER PRACTICE ANOTHER wo wave described by wave functions El = 4.60 sin mm + 7 and E = 7.60 sin 10m: sum to give the resulting wave E + E = E sin 101K + . Determine the required value for the following. 2 1 2 S 2 (3) Es Es = x Can you write an expression for the sum of the two wave functions E1 and 52? You will find the trig identity sin(u :i: [1) = sin n: cos [1 1 cos a sin I? useful. Try using the trig identity on both the given wave functions and on the known form of the result, then compare terms to see if you can solve for the unknowns. (b ) 02 a: = 3: Can you write an expression for the sum of the two wave functions E1 and 52? You will find the trig identity sin(u :i: [1) = sin a cos [1 1 cos a sin I? useful. Try using the trig identity on both the given wave functions and on the known form of the result, then compare terms to see if you can solve for the unknowns. 10. [0/1 Points] PREVIOUS ANSWERS WAUNIPHYSAV1 35.P.030. ASK YOUR TEACHER PRACTICE ANOTHER Two waves are represented by the wave functions E1 = E0 sin wt and E2 = ZED sin(wt + (p), where E0 = 1.40 pV/m and o) = 2.50 x 1015 rad/s. They interfere at a point where the phase difference is g; = 53.0. The resultant wave function El + 52 is expressed in the form ER sin(mt + In). Use a phasor diagram to determine the amplitude ER, and phase angle a for the resultant wave. x ER = Draw a phasor diagram (at some time t) showing the amplitude of both wave functions (EO and 250), the phase difference at between the two wave functions, the amplitude of the resultant wave function ER, and the phase difference a for the resultant wave function. Referring to the phasor diagram, see if you can use the law of cosines to determine the amplitude of the resultant wave function. uV/m 4. [0.5/1 Points] PREVIOUS ANSWERS WAUNIPHYSAV1 35.P.023. ASK YOUR TEACHER PRACTICE ANOTHER Coherent light of wavelength A = 535 nm passes through a double slit and the resulting interference pattern is viewed on a screen. At a point on the screen, the intensity of the interference pattern is 68.0% of the intensity at the central maximum. In order to produce this result on the screen, determine the following for the light arriving from the two slits. (a) minimum phase difference 1.20 V rad (b) minimum path difference 10000 x How is the path difference related to the phase difference and the wavelength? nm 5. [-I1 Points] WAUNIPHYSAV1 35.P.022. ASK YOUR TEACHER PRACTICE ANOTHER Coherent light of wavelength 1. = 580 x 10'9 m, angular frequency w = 3.25 x 1015 rad/s, and amplitude E0 passes through three parallel slits a distance d = 2.40 x 10'4 m apart and produces an interference pattern on a screen a distance L = 2.20 m away. If we represent the light from these three slits by the wave functions El = Eo sin wt, E2 = E0 sin(wt + (a), and E3 = E0 sin(a)t + Za), it can be shown that the intensity I, which is proportional to the square of the resultant electric eld Es, can be expressed as I