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What is the separation between two slits for which 610-nm orange light has its first maximum at an angle of $30.0^\circ$?
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$1.22 \textrm{ }\mu\textrm{m}$
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OpenStax College Physics for AP® Courses Solution, Chapter 27, Problem 8 (Problems & Exercises) (1:00)

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Video Transcript
This is College Physics Answers with Shaun Dychko. During a double slit experiment, we are using light of wavelength 610 nanometers and the first maximum occurs at a angle of 30.0 degrees so m in this formula here for the locations of the constructive interference or the maxima m is going to be 1 because it's the first maximum, d is the separation between the slits that we have to find. So we are going to divide both sides by sin of 30 and that gives us d equals the order times the wavelength of light divided by sin of the angle to the maximum... I suppose I should put a Θ there. Okay! So the order is 1 because it's the first maximum and we multiply that by 610 nanometers divided by sin of 30 and that's 1220 nanometers, which is 1.22 micrometers.