Two slits spaced 0.260 mm apart are 0.900 m from a screen and illuminated by coherent light of wavelength 660 nm. The intensity at the center of the central maximum 1u = 0°2 is I0. What is the distance on the screen from the center of the central maximum (b) to the point where the intensity has fallen to I0>2?

Video transcript

Hello, fellow physicists today, we're going to solve the following practice problem together. So first off, let's read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A monochromatic light lambda equals nanometers is used in a young's double slit experiment which consists of two slits that are spaced 0. millimeters apart, light waves from these slits interfere constructively and destructively on the screen that is 0. m from the slits to produce bright and dark fringes. The intensity at the center in the Y DS experiment is I subscript zero I zero, determine the distance from the center of the central max Maximus C when the intensity has decreased to I zero, divided by two. OK. So we're given some multiple choice answers. Let's read them off to see what our final answer might be. A is 0.05 centimeters. B is 0.65 millimeters C is 0. millimeters and D is 0.07 centimeters. OK. So first off, let us recall the equation for the intensity of a two source interference pattern which states that the intensity I is equal to I subscript zero I zero multiplied by cosine squared of pi multiplied by lower case D multiplied by Y divided by lambda multiplied by D. OK. Where D capital D is the distance between the double slit. So this is capital D, the distance between the double slit and the screen, lower case D is the separation distance between the two slits. Lower case Yy is the value that we're trying to determine. That's our end goal. It's the distance from the center of the Central Maxima Sea. And Lambda represents the wavelength. Let's also note that the problem also said that, that I, the intensity is equal to one half multiplied by I zero. So let's plug in one half I zero for I into our intensity equation. So when you plug it in, it will look something like this. OK? So it'd be one half I zero equals I zero cosine squared cosine squared of pi multiplied by D multiplied by Y divided by Lambda capital D. OK. So we can use algebra to simplify this equation to the following high, divided by four radiant is equal to hi multiplied by lower case D multiplied by Y divided by Lambda multiplied by capital D. So at this stage, we need to rearrange this equation and solve for Y. So let's do that. So Y equals and just using algebra again, we can rearrange the software Y so lamb so Y equals LAMBDA multiplied by D capital D I should say divided by four multiplied by lower case D. So at this stage, we can plug in are known variables to solve for A Y. So let's do that. So the wavelength is 630 nanometers, but we need to convert nanometers to meters. So all we have to do to do that is take 630 multiply it by 10 to the power of negative nine to get it into meters. So 600 130 multiplied by 10 of the power of negative 9 m multiplied by capital D. The distance between the double slit and the screen which has given us given to us in the problem as 0.59 m divided by or multiplied by lower case D which is the separation distance of the two slits which is given to us as 0.31 millimeters, but we need to convert millimeters to meters. So all we have to do is just take 0.31 multiplied by 10 to the power of negative three meters. Awesome. So when we plug that into a calculator, the value for Y that we should get is 0.028. It's 0. 299 meters. But we need to convert meters to millimeters. So we can use dimensional analysis to convert meters to millimeters. So let's recall that there's millimeters and 1 m meters cancel out leaving us with millimeters. So our new answer should be zero point in rounding 0.30 millimeters. So Y equals 0.30 millimeters hurray we did it. So that means our final answer has to be C 0.30 millimeters. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.