The glass rod of Exercise 34.22 is immersed in oil (n = 1.45). An object placed to the left of the rod on the rod's axis is to be d 1.20 m inside the rod. How far from the left end of the rod must the object be located to form the ?

Video transcript

Hi, everyone in this practice problem, we're being asked to determine the position of an object from the hemispherical surface. We will have a transparent cylinder with a radius of R equals to four centimeter made out of crown glass with an index of refraction of 1.52. The cylinder lies entirely on the bottom of a container filled with water with the end water of 1.33 or index of refraction of water to be 1.33. And the boundary between the crown glass and the water is a convex hemispherical surface with a radius of 1.5 centimeter. An object located to the left of the hemispherical surface forms an image on the cylinder axis 60 centimeter inside of the cylinder. And we will be asked to determine the position of the object from the hemispherical surface. The options given are a one point oh one centimeter to the left of the surface. B 9.57 centimeter to the left of the surface c 13.1 centimeter to the left of the surface. And lastly d 14.6 centimeter to the left of the surface. So the object image relationship for a spherical refracting surface is going to be given by the equation of N water divided by S plus and less divided by as apostrophe will be equals to and minus and water all of that divided by R. So in this case, we are given that the glass is going to equals to 1.52 water is going to equals to 1.33 R is going to be the radius of the curvature of the hemispherical surface, which is given to be 1.5 centimeter. And it uh apostrophe is going to be the image distance which is given to be 60 centimeters. S is the possession of the object from the hemispherical surface which is the um variable that we are interested to find. So we actually have all of the other information other than S. So we can actually substitute all of this information into our equation in order for us to then solve for S. So first we have N water which is 1.33 divided by S or the position of the object from the hemispherical surface plus N glass, which is 1.52 divided by S apostrophe which is centimeter equals to N glass which is 1. minus N water, which is 1.33 all of that is divided by the R which is 1.5 centimeter. And then we will then get 1. divided by S to be equals to 0.1 oh 13 and then rearranging things and calculating you will then get s to then be 13.1 centimeter. In this case, as long as everything in the same unit, meaning the S as apostrophe and R as in the same unit, it doesn't really matter. So in this case, because the S apostrophe and the R R M centimeter, then our S is also going to be in centimeter. So in this particular practice problem, then we will get the object or the distance of the object placed 13.1 centimeter to the left of the hemispherical surface will actually give us this particular condition and that will be corresponding to option C in our answer choices. So option C where the object is placed 13 point centimeter to the left of the hemispherical surface will be the answer to this particular practice problem. So that will 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 and that'll be it for this one. Thank you.