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 the waves reaching point P from the edges of the slit will be equal to the distance between the edges times sine of the angle between the center of the slit and point P. Since we are at the second minimum, this angle is approximately equal to the angle between the first minimum and the center of the slit, which is given by $\sin	heta=\frac{\lambda}{a}$, where $\lambda$ is the wavelength and $a$ is the width of the slit. Therefore, the path length difference is given by $d=(PX)-(PY)=a\sin	heta=a\frac{\lambda}{a}=\lambda$. Note that option D gives this value correctly with the correct units.

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