The diagram shows a single slit with the direction to a point P on a distant screen (not shown). At P, the pattern has its second minimum (from its central maximum). If X and Y are the edges of the slit, what is the path length difference (PX) - (PY)?
A) $\lambda$/2
B) $\lambda$
C) 3$\lambda$/2
D) 2$\lambda$
E) 5$\lambda$/2

Question

The diagram shows a single slit with the direction to a point P on a distant screen (not shown). At P, the pattern has its second minimum (from its central maximum). If X and Y are the edges of the slit, what is the path length difference (PX) - (PY)? 
A) $\lambda$/2 
B) $\lambda$ 
C) 3$\lambda$/2 
D) 2$\lambda$ 
E) 5$\lambda$/2

Quizplus · Accepted Answer

The path length difference between two waves, which interfere destructively at the second minimum, is equal to the distance traveled by one wave more than the other to reach that point. In this case, as the second minimum is formed, the wave that reaches point P traveled an additional half of the wavelength compared to the wave that reaches point Y. Therefore, the path length difference (PX) - (PY) = 2d/2 - d/2 = d/2, which is equal to F1F1F1S1F1F1F10. Thus, the answer is (D).

The Diagram Shows a Single Slit with the Direction to a Point