SAT Subject Physics Practice Question 286: Answer and Explanation
57. Consider a double-slit interference experiment using yellow light of wavelength λ, with the slits labeled S1 and S2. If P is the center of a dark fringe on the screen on which the resulting diffraction pattern is projected, which of the following equations relating S1P and S2P, the distances from slits S1 and S2, respectively, to the point P could be true?
A. S1P – S2P = λ
B. S1P – S2P = λ
C. S1P – S2P = 2λ
D. S1P – S2P = 3λ
E. S1P = S2P
Correct Answer: A
Since P is the center of a dark fringe, it is a location of completely destructive interference. In order for this to occur, the waves must be exactly out of phase when they reach P. This will happen if the difference between their path lengths from the slits is an odd number of half wavelengths. Only the equation in A satisfies this requirement.