PROBLEMS FOR MODULE 3: OPTICS AND WAVE PHENOMENA 1) Give a description of a traveling wave How to distinguish between transverse waves and longitudinal waves? 2) Give a definition of wave interference What are coherent wave sources? Distinguish between two types of wave interference and give the conditions for them to occur 3) Give a definition of wave diffraction Write the formula to determine minima for a single - slit diffraction pattern 4) Give description of a diffraction grating Why is a diffraction grating the tool of choice for separating the colors of light? 5) Give a definition and describe the operation of a spectroscope What is the most important component of a spectroscope? 6) Give briefly the classification of light spectra according to their origin or mechanism of excitation 7) The equation of a transverse traveling wave to the right on a string is y(x, t) = 2.0 cm sin(0.50π cm-1x – 200π s-1 t) Find the wave amplitude, wavelength, period, frequency, velocity Ans A = 2.0 cm; λ = 4.0 cm; T = 0.01 s; f = 100 s-1; v = 40 cm/s 8) Figure 1a below represents a wave at t = traveling along a rope to the right Figure 1b below represents the same wave at t = 10 s (a fraction of the period T) (1) Find: (a) the wavelength of the wave, (b) the frequency of the source that produces the wave, (c) the velocity of the wave (2) Write an equation for the wave shown in Fig that gives the displacement y as a function of x and t Ans 1) (a) 4.00 cm; (b) 0.05 Hz; (c) 0.20 cm/s 2) y (x, t) = 10 cm sin [(πx/2)cm-1 − (0.1πt)s-1] 9) Two point sources, 3.0 cm apart, are generating periodic waves in phase A point on the third antinodal line of the wave pattern is 10 cm from one source and 8.0 cm from the other source Determine the wavelength of the waves Ans 0.667 cm 10) Two point sources are generating periodic waves in phase The wavelength is 4.0 cm A point on the second antinodal line is 30.0 cm from the nearest source How far is this point from the farthest source? Ans 38 cm 11) Two point sources are generating periodic waves in phase The wavelength of the waves is 3.0 cm A point on a nodal line is 25 cm from one source and 20.5 cm from the other Determine the nodal line number Ans Second nodal line 12) Two point sources are generating periodic waves in phase A point on the fourth nodal line is 25.0 cm from one source and 39.0 cm from the farthest source Determine the wavelength Ans 4.0 cm 13) To illustrate some typical results from Young’s double-slit interference, consider the sample data provided below for d, y, L and n Data table Slit separation (d) Distance from Slits to Screen (L) Distance from AN0 to AN4 (y) Order value (n) 0.250 mm 9.78 m 10.2 cm (Note: AN0 = central antinode and AN4 = fourth antinode) Determine the wavelength Ans 6.52 x 10-7 m 14) The diagram below depicts the results of Young's experiment The appropriate measurements are listed on the diagram Use these measurements to determine the wavelength of light in nanometers (GIVEN: meter = 109 nanometers) Ans 657 nm 15) Light of wavelength 587.5 nm illuminates normally a single 0.75-mm-wide slit (a) At what distance from the slit a viewing screen should be placed if the first minimum of the diffraction pattern is to be 0.85 mm from the central maximum? (b) Calculate the width of the central maximum Ans (a) 1.1 m; (b) 1.7 mm 16) A light source emits two major spectral lines, an orange line of wavelength 610 nm and a blue-green line of wavelength 480 nm If the spectrum is resolved by a diffraction grating having 5000 lines/cm and viewed on a sreen 2.00 m from the grating, what is the distance (in centimeters) between the two spectral lines in the second - order spectrum? Ans.: θ1 = 37.6 o and θ2 = 28.7 o; ∆y = L(tanθ1 − tanθ2) = 44.5 cm