What is the wavelength of light falling on double slits separated by $2.00\mu \text{m}$ if the third-order maximum is at an angle of $60.0^{\circ }$?

Video Transcript

This is College Physics Answers with Shaun Dychko. We want to know the wavelength of light that has a third order maximum at an angle of 60 degrees that is going through two slits separated by two micrometers. So, our formula for the maxima through a double slit is the separation between the slits times sine of the angle to the maximum equals the maximum order times the wavelength. And so, we'll solve for Lambda by dividing both sides by M here and then switch the sides around. And then the wavelength, then, is the separation between slits times sine of the angle divided by the order. So, that's six micrometers, which is written as times ten to the minus six meters, times sine of 60 degrees divided by three, because it's the third order maximum, and this gives 577 nanometers must be the wavelength of the light.