Inferring Shape of Phasors in Multi-Slit Diffraction

[hidemi]

Homework Statement

At a bright diffraction line phasors associated with waves from the slits of a multiple-slit barrier:
A. are aligned
B. form a closed polygon
C. form a polygon with several sides missing
D. are parallel but adjacent phasors point in opposite directions
E. form the arc of a circle

The correct answer is A

Relevant Equations

d * sin(theta) = m * lambda

I know that phasors of a single-slit diffraction form a closed polygon or circle, but how could we infer the shape when phasors generated by slits of a multiple-slit barrier?

 

[Charles Link]

The $m \lambda=d \sin{\theta}$ for constructive interference is sort of on the right track, but what you are needing is the phase angle between phasors from adjacent sources a distance $d$ apart: $\phi=(\frac{2 \pi}{\lambda}) d \sin{\theta}$. Using the first expression, (since you are told that the sources constructively interfere), what can you say about $\phi$? Will the phasors be aligned?

 

[Steve4Physics]

I know that phasors of a single-slit diffraction form a closed polygon or circle ...

Closed polygon's give minima (zero intensity), not maxima.

Think of adding phasors in the same way as adding vectors. The resultant is zero only when the vectors form a closed polygon.

There is an important difference between a single-slit and multiple-slits when using phasors.

For a single-slit analyis, each point in the aperture has a phasor. The phasors are aligned in only one situation - for the central direction.

For a multiple-slit analysis we associate each slit with a single phasor. A maximum is produced whenever the phasors are aligned (unlike a single-slit).

This video gives quite a good insight. You need to compare the single-slit and double-slit simulations carefully.

 

[hidemi]

Closed polygon's give minima (zero intensity), not maxima.

Think of adding phasors in the same way as adding vectors. The resultant is zero only when the vectors form a closed polygon.

There is an important difference between a single-slit and multiple-slits when using phasors.

For a single-slit analyis, each point in the aperture has a phasor. The phasors are aligned in only one situation - for the central direction.

For a multiple-slit analysis we associate each slit with a single phasor. A maximum is produced whenever the phasors are aligned (unlike a single-slit).

This video gives quite a good insight. You need to compare the single-slit and double-slit simulations carefully.

Thank you! I got it