Question

At what angle is the fourth-order maximum for the situation in Exercise 27.6?

$2.06^\circ$

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Video Transcript

This is College Physics Answers with Shaun Dychko. 450 nanometer wavelength light is incident on a double slit where the slits are separated by 0.0500 millimeters and we are asked to figure out the angle to the fourth order maximum. Let's first convert units into meters so we have 450 nanometers is 450 times 10 to the minus 9 meters and our separation between slits is 0.0500 times 10 to the minus 3 meters; this is the formula for the maxima where you have the separation between slits

*d*times*sin*of the angle to the maximum equals the order of the maximum times the wavelength of the light and we will divide both sides by*d*to solve for*sin Θ*and then take the inverse*sin*of both sides to solve for*Θ*. So*Θ*is the inverse*sin*of the order times the wavelength divided by the separation between slits. So that is the inverse*sin*of 4 times 450 times 10 to the minus 9 meters divided by 0.0500 times 10 to the minus 3 meters which is 2.06 degrees.