Counting Double Slit Maxima

One of my friends works at a university on the quarter system, and he mentioned that his students are taking their final exams soon. I am going to put off my post on the diffusion equation until next week, and instead, write a couple of optics posts that will hopefully help students with the material on their introductory physics final exams. This first post showcases a video that I made a couple of years ago. It describes the prcodeure that is used to find the theoretical maximum number of bright spots for a given double slit experiment.

The trickiest part about this problem is determining the correct value for \(m\). For example, suppose I give you a set up where the slit distance \(d = 3.0 \mu m\) and the incident wavelength of light is \(620 nm\) (corresponding to red light). Then:

\[\begin{equation} total = \frac{d}{\lambda} = \frac{3.0 \mu m}{620 nm} = 4.8 \end{equation}\]

If you immediately double this number and add one, you get:

\[\begin{equation} 2(4.8) + 1 = 10.6\hspace{6mm}(INCORRECT) \end{equation}\]

Thus, you might incorrectly say that there are 10 or 11 bright spots that could theoretically be seen on the screen. However, if you properly round down, your answer becomes:

\[\begin{equation} 2(4) + 1 = 9\hspace{6mm}(CORRECT) \end{equation}\]

And you see that there are only nine bright spots that can possible be projected onto this screen.

Be careful with your \(m\)’s!