Hello, everyone. This is problem twice. Seven from Chapter 28. It says the interference pattern shown in the Figure party of the figure's produced by green light with a wavelength that's given to us Lambda equals 505 Miami years passing through two slits. The separation 127 micro meters. After passing through the slits, light forms a pattern of bright and dark spots on screen. Located 1.25 million slits. A what is the distance between the two vertical dashed lines? Okay, so if we go ahead and look at this figure, we see that there are basically six bright dots or six dots that indicate the bright spots I want to three for I've six like so something like that. And the dash lines go here and here through ah maximum. And then through a minimum over here, that's 12345 minimum. It's the fifth minimum to the right of this. This maximum. Okay, so it says, What's the distance between the lines? Well, we can use our our double slits equation for, um, minimal here because now we're being given Lambda and D and this problem and we can just count out our M because our M should be five and then using this using the single fado that we find here we can find the distance between the two using L attention to Florida. And so if we do this, so theta is just the arc sine off. Linda, Time's gonna defend mice 1/2 over D. This is approximately 1.0 to 5 degrees and then plugging that in here along with using the L. Given the problem, we guess 2.24 centimeters now all this was part, eh, Burt? Be ah says if it is desired to produce a more tightly packed interferes pattern, should the frequency of light be increased or decreased. So if we wanted the interference pattern to be more tightly packs, we would want sign of theater. Well, we would want fated to go down. They did to decrease Seita to decrease. And ah, if they did decreases, that means that the sign inflated decreases because our fate is just between zero and 90 degrees. So as stated decreases sign if they're decreases. So on this side must decrease. Um, of course. Ah, if we want this too tightly packed together. We'll think about leaving M the same and making fate of smaller. So animals the same deal stay the same because that's just ah, physical perimeter. And then ah, so that means that Lambda must go down. We're not asked about Linda were actually asked about F. But since F is equal to see over Lambda, this means that f must go up. So in order to do that frequency must be increased.