Two identical light waves, A and B, are emitted from different sources and meet at a point P. The distance from the source of A to the point P is L_A; and the source of B is a distance L_B from P. Which one of the following statements is necessarily true concerning the interference of the two waves? A)A and B will interfere constructively because their amplitudes are the same. B)A and B will interfere constructively if L_A = L_B. C)A and B will interfere destructively if L_A - L_B = m$\lambda$ where m = 0, 1, 2, 3, ... D)A and B will interfere destructively if L_A is not equal to L_B. E)A and B will interfere constructively because their wavelengths are the same.

Question

Quizplus · Accepted Answer

The interference between two waves depends on the phase difference between them. If the waves are in phase, they interfere constructively; if they are out of phase, they interfere destructively. The phase difference between two waves is determined by the path difference, which is the difference in distance traveled by the waves from their sources to the point of interference. If the path difference is an integer multiple of the wavelength, the waves are in phase, and they interfere constructively. If the path difference is an odd multiple of half the wavelength, the waves are out of phase, and they interfere destructively. In this case, the two waves are identical, so their amplitudes are the same. The only difference between them is the path they travel from their sources to the point of interference, which is given by the distances L_A and L_B. If these distances are equal, the path difference is zero, and the waves are in phase, so they interfere constructively. If the distances differ by an even multiple of the wavelength, the path difference is an integer multiple of the wavelength, and the waves are in phase, so they interfere constructively. If the distances differ by an odd multiple of half the wavelength, the path difference is an odd multiple of the wavelength, and the waves are out of phase, so they interfere destructively. Therefore, choice B is necessarily true.

Two Identical Light Waves, a and B, Are Emitted from Different