Principal and Secondary Maxima in Multiple-Slit Interference

All flashcards

Adjacent-slit path difference

For slit spacing $d$ and observation angle $\theta$, it is $d\sin\theta$.

Principal maximum

A bright fringe where contributions from all slits reinforce in phase.

Secondary maximum

A weaker bright fringe between principal maxima, formed when contributions partly cancel.

Secondary-maximum count

An ideal array of $N$ equally spaced coherent slits has $N-2$ secondary maxima between principal maxima.

Three-slit half-wavelength case

If adjacent rays differ in path by $\lambda/2$, the intensity is $1/9$ of a principal maximum.

Quiz questions

1. For slits separated by $d$, what is the path difference between adjacent rays observed at angle $\theta$?Answer: $d\sin\theta$
2. Which condition gives a principal maximum for slit spacing $d$ and wavelength $\lambda$?Answer: $d\sin\theta=m\lambda$, with integer $m$
3. With three slits and an adjacent-ray path difference of $\lambda/2$, why is there still light at that angle?Answer: Two contributions cancel, while the third remains uncanceled.
4. For an ideal array of $N$ equally spaced coherent slits, how many secondary maxima lie between neighboring principal maxima?Answer: $N-2$
5. For equal coherent slit contributions, what happens to principal maxima as the number of slits increases?Answer: They become narrower and their peak intensity increases.