Question

Find the angle for the third-order maximum for 580-nm- wavelength yellow light falling on a diffraction grating having 1500 lines per centimeter.

$15.1^\circ$

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This is College Physics Answers with Shaun Dychko. 580 nanometer light is passing through a diffraction grating that has 1 centimeter between every 1500 lines and that we can figure out the amount of centimeters between each line by dividing these two numbers. So it's 1 times 10 to the minus 2 meters divided by 1500 lines and that's 6.667 times 10 to the minus 6 meters between each line so it's about 6.7 micrometers between each line and we want to know what is the angle to the third order maximum in the pattern on the screen that's behind the diffraction grating? So we have this formula for figuring that out this is the separation between each line in the diffraction grating times

*sin*of the angle to the maximum and that equals the order of the maximum times the wavelength of light that we are dealing with and we'll solve this for*sin Θ*by dividing both sides by*d*so*sin Θ*is*mλ*over*d*and then take the inverse*sin*of both sides to solve for*Θ*. So*Θ*is the inverse*sin*of the order, which is 3 times the wavelength, which is 580 times 10 to the minus 9 meters divided by the distance between slits and the diffraction grating and that's 6.667 times 10 to the minus 6 meters and the angle then is 15.1 degrees to the third order maximum.