A person is lying on a diving board 3.00 m above the surface of the water in a swimming pool. She looks at a penny that is on the bottom of the pool directly below her. To her, the penny appears to be a distance of 7.00 m from her. What is the depth of the water at this point?

Video transcript

Hi, everyone in this practice problem, we are being asked to determine the depth of the water. We will have a child sitting out on a tree branch that reaches across the river and is six m above the river's surface. While on the top, the child spots a shopping trolley at the bottom of the river right below him. The distance between him and the trolley looks like 50 m. And we're being asked to determine the depth of the water or how deep the water is considering that the water surface is acting like a spherical surface with an infinite radius of curvature. The options given for the depth of the water is a 8.77 m b 11.97 m C 14.51 m and lastly d 16. m. So first, what we wanna do is to find the distance below the water off the trolley or the distance from the water to the trolley as seen by the child. So in this case, uh the distance is then going to be below water scene by child. So we know that um it looks like the distance between the child and the trolley is 15 m. So I'm gonna write down 15 m and we wanna subtract the distance from the water surface to the child itself, which is given to be six m in the problem statement. So that will give us the distance from the water surface through the trolley as seen by the child, which is going to then be nine m. Next, we wanna take a look at the convention that we have at which nine m is the image distance of the trolley where in this case, the image is going to be nine m below the surface of the water or on the other side of the actual child, which in this case, as apostrophe is then going to be negative nine m. So it is given in the problem statement that the water surface is acting like a spherical surface with an infinite radius of curvature. So the surface of water is treated like a spherical surface with an infinite radius of curvature which will then give us a one over F to be equals to one over infinity which will give us zero. So we want to recall the formula that we wanna use for this particular problem which is going to be an A divided by S plus and B divided by S apostrophe to be equals to zero. In this case, we know that uh we are dealing with two different medium which is water and air and the end of air is going to be, I'm gonna write that down as and B and in this case, that will then equals to one and the end of the water will be an A and in this case will be equals to 1.333. So it will be the opposite because the image is on the water side. So what's on top is going to be the end of the air. All right. So now we can actually substitute our, our information given here. Um in order for us to get the actual depth of the water, what we wanna do is to actually get the S. So in this case, by rearranging our equation here will then equals to negative and A divided by N B multiplied by S apostrophe. So now let's substitute all of our known information. So we will have negative and A which is negative 1.333. And then we have that divided by N B which is just one multiplied everything with apostrophe which we have determined is going to be negative nine m. So in this case, calculating all of this, we will then get our S value or the depth of the water, which will actually then be 11.97 m. So the depth of the water is 11.97 m or our value is going to be 9 11.97 m, which will correspond to option B in our answer choices. So option B will be the answer to this particular practice problem and that'll be it for this video. If you guys still have any sort of confusion, please make sure to check out our other lesson videos on similar topics, but they'll be it for this one. Thank you.