\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)

Two-Slit Interference

The formula we want is $$y(n)={n\lambda L\over d}$$ where

• $\lambda$ is the wavelength of the light, usually measured in nanometers ($1\u{nm}=10^{-9}\u{m}$)
• $d$ is the distance between the slits (often measured in millimeters: $1\u{mm}=10^{-3}\u{m}$)
• $L$ is the distance from the slits to the screen where the pattern is projected
• $y$ is the distance from the center of the screen to the $n$th bright spot
• $n$ is the order of the bright spot you want to find

Possible pitfalls

• Confusing the different lengths in the problem
• Forgetting to convert all lengths to meters
• Forgetting that $d$ is the distance between the slits, not the width of each slit. (That would be $a$.)
• Confusing this with Diffraction Patterns, where $y$ is the position to the dark spots

Recommendation

Start the problem with a table like

$\lambda=$	___
$d=$	___
$L=$	___
$n=$	___
$y=$	___

fill in the values you know, and indicate the value that you need. Convert all of these to meters, substitute into the equation above, and then solve.