Question

What is the spacing between structures in a feather that acts as a reflection grating, given that they produce a first- order maximum for 525-nm light at a $30.0^\circ$ angle?

$1.05\textrm{ }\mu\textrm{m}$

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Video Transcript

This is College Physics Answers with Shaun Dychko. A bird feather acts as a reflection grating and produces a first order maximum at an angle of 30.0 degrees for 525 nanometer light. So this is the formula for the maxima in a diffraction pattern and the spacing between lines and the diffraction grating multiplied by

*sin*of the angle to the maximum equals the order of the maximum times the wavelength of the light. So we can solve for*d*here which will be the spacing between the features and the feather that are acting as a grating and we divide both sides by*sin Θ*and so*d*is the order times the wavelength divided by*sin*of the angle. So that's 1 times 525 nanometers divided by*sin*30.0 and since we use nanometers here for the wavelength, our answer is in nanometers—1050— and we'll convert this into micrometers just because that's a more traditional way of writing a number like this... multiply by 1 micrometer for every 1000 nanometers and we have 1.05 micrometers.