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Question
What is the highest-order maximum for 400-nm light falling on double slits separated by $25.0 \textrm{ }\mu\textrm{m}$.
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Final Answer
62
Solution Video

OpenStax College Physics Solution, Chapter 27, Problem 13 (Problems & Exercises) (1:44)

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Video Transcript

This is College Physics Answers with Shaun Dychko. We want to know the highest order maximum that's possible for 400 nanometer light falling on slits separated by 25 micrometers. So, the highest order maximum will occur at an angle of 90 degrees. If you have two slits and there's a screen over here, the maximum angle you can possibly achieve between the slits in the screen is going to be 90 degrees. I mean, precisely 90 degrees, you won't see anything on the screen, but that's the threshold between when you will and will not see something. So, we'll solve for <i>M</i> with <i>Theta</i> equals 90 and we'll take the floor of the number, which is sort of a programming way of saying this number will round down always. Okay, we'll talk about that in a second. So, the formula for the maxima with Young's double slit experiment is the separation between slits times sine <i>Theta</i> equals the order multiplied by the wavelength. And, we'll solve for <i>M</i> by dividing both sides by <i>Lambda</i>. And so, <i>M</i> is <i>D</i> sine <i>Theta</i> over <i>Lambda</i>. So, the separation between slits is 25 micrometers written as times ten to the minus six meters multiplied by sine of 90 because we're solving for the highest order of maximum possible, divided by 400 times ten to the minus nine meters and this gives 62.5. Now, the order has to be an integer and we can think of either 62 or 63. But, 63 will be beyond 90 degrees and so that doesn't make any sense. Light won't fall on the screen. And so, we always round down. This is the floor of the number, 62.