Chapter #4 Solutions - Introduction to Optics - Leno M Pedrotti, Leno S Pedrotti, Frank L Pedrotti - 3rd Edition

 

1. A pulse of the form ... is formed in a rope, where a and b are constants and x is in centimeters. Sketch this pulse. Then write an equation that represents the pulse moving in the negative direction at 10 cm/s. Get solution

2. A transverse wave pulse, described by ...is initiated at t = 0 in a stretched string.a. Write an equation describing the displacement y(x, t) of the traveling pulse as a function of time t and position x if it moves with a speed of 2.5 m/s in the negative x-direction.b. Plot the pulse at t = 0, t = 2 s, and t = 5 s. Get solution

3. Consider the following mathematical expressions, where distances are in meters:1. y(z, t) = A sin2[4π (t/s + z/m)]2. y(x, t) = A(x/m− t/s)23. y(x, t) = A/(Bx2− t)a. Which qualify as traveling waves? Prove your conclusion.b. If they qualify, give the magnitude and direction of the wave velocity. Get solution

4. If the following represents a traveling wave, determine its velocity (magnitude and direction), where distances are in meters. ... Get solution

5. A harmonic traveling wave is moving in the negative z-direction with an amplitude (arbitrary units) of 2, a wavelength of 5 m, and a period of 3 s. Its displacement at the origin is zero at time zero. Write a wave equation for this wave (a) that exhibits directly both wavelength and period; (b) that exhibits directly both propagation constant and velocity; (c) in complex form. Get solution

7. For a harmonic wave given by y = (10 cm) sin[(628.3/cm)x − (6283/s)t]determine (a) wavelength; (b) frequency; (c) propagation constant; (d) angular frequency; (e) period; (f) velocity; (g) amplitude. Get solution

8. Use the constant phase condition to determine the velocity of each of the following waves in terms of the constants A, B, C, and D. Distances are in meters and time in seconds. Verify your results dimensionally.a. f(y, t) = A(y − Bt)b. f(x, t) = A(Bx + Ct + D)2c. f(z, t) = A exp(Bz2+ BC2t2−2BCzt) Get solution

9. A harmonic wave traveling in the +x-direction has, at t = 0, a displacement of 13 units at x = 0 and a displacement of −7.5 units at x = 3λ/4. Write the equation for the wave at t = 0. Get solution

11. By finding appropriate expressions for ..., write equations describing a sinusoidal plane wave in three dimensions, displaying wavelength and velocity, if propagation isa. along the +z-axisb. along the line x = y, z = 0c. perpendicular to the planes x + y + z = constant Get solution

12. Show that if ... is a complex number,(a) ...;(b) ...;(c) ...;(d) sin θ = (eiθ − e−iθ)/2i. Get solution

13. Show that a wave function, expressed in complex form, is shifted in phase (a) by π/2 when multiplied by i and (b) by 77 when multiplied by −1. Get solution

14. Two waves of the same amplitude, speed, and frequency travel together in the same region of space. The resultant wave may be written as a sum of the individual waves. ψ/(y, t) = A sin(ky + ωt) + A sin(ky − ωt + π)With the help of complex exponentials, show that ψ(y, t) = 2A cos(ky)sin(ωt) Get solution

15. The energy flow to the earth’s surface associated with sunlight is about 1.0kW/m2. Find the maximum values of E and B for a wave of this power density. Get solution

16. A light wave is traveling in glass of index 1.50. If the electric field amplitude of the wave is known to be 100 V/m, find (a) the amplitude of the magnetic field and (b) the average magnitude of the Poynling vector. Get solution

17. The solar constant is the radiant flux density (irradiance) from the sun at the surface of the earth’s atmosphere and is about 0.135 W/cm2. Assume an average wavelength of 700 nm for the sun’s radiation that reaches the earth. Find (a) the amplitude of the ...- and ... -fields; (b) the number of photons that arrive each second on each square meter of a solar panel; (c) a harmonic wave equation for the ...-field of the solar radiation, inserting all constants numerically. Get solution

18. a. The light from a 220-W lamp spreads uniformly in all directions. Find the irradiance of these optical electromagnetic waves and the amplitude of their ...-field at a distance of 10 m from the lamp. Assume that 5% of the lamp energy is converted to light.b. Suppose a 2000-W laser beam is concentrated by a lens into a cross-sectional area of about 1 × 10−6 cm2. Find the corresponding irradiance and amplitudes of the ...- and ...-fields there. Get solution

19. Show that, in order to conserve flux, the amplitude of a cylindrical wave must vary inversely with .... Get solution

20. Show that Eq. (4-45) for the Doppler effect follows from Eq. (4-44) when υ ≪ c. Get solution

21. How fast does one have to approach a red traffic light to see a green signal? So that we all get the same answer, say that a good red is 640 nm and a good green is 540 nm. Get solution

22. A quasar near the limits of the observed universe to date shows a wavelength that is 4.80 times the wavelength emitted by the same molecules on the earth. If the Doppler effect is responsible for this shift, what velocity does it determine for the quasar? Get solution

23. Estimate the Doppler broadening of the 706.52-nm line of helium when the gas is at 1000 K. Use the root-mean-square velocity of a gas molecule given by ...where R is the gas constant, T the Kelvin temperature, and M the molecular weight. Get solution

24. Consider the electric field, ...Produce plots like those in Figure 4-12 that show the evolution of the electric field vector, at the plane z = 0, as a function of time over one complete temporal cycle for the following cases.a. Ex = 2Ey, φ0x = φ0y= 0b.Ex = 2Ey, φ0x = 0, φ0y= π/2c. Ex = 2Ey, φ0x = 0, φ0y = −π/2d. Ex = 2Ey, φ0x = π/4, φ0y = −π/4e. Ex = 2Ey, φ0x = 0, φ0y = −π/4 Get solution