An object is 18.0 cm from the center of a spherical silvered-glass Christmas tree ornament 6.00 cm in diameter. What are the position and magnification of its ?

Video transcript

Welcome back. Everyone. We are told that a scale model is placed at 15 centimeters to the left of the center of a reflective sphere. Now, the radius of our reflective sphere is eight centimeters and we were tasked with finding with two different things. One, what is, where is the image of the car going to be located? And the magnification factor. What is that going to be on the car? Well, what we can say is that the position of the object is going to be 15 centimeters minus the radius of the sphere which is seven centimeters. And since we were given the radius of curvature, we can say that our focal point is simply the negative of our radius divided by two, which gives us negative four centimeters. With that being said, what we can say is that the position of the image position of the image plus the position of the object or one over the position of the object is equal to one over our focal point. Solving for one over S prime, we get one over F minus one over S which gives us that S prime is equal to S F divided by S minus F. So let's go ahead and calculate that we have seven centimeters times negative four centimeters divided by seven minus negative four, which gives us negative 2.55 centimeters for the position of the image in reference to the edge of the sphere. But we want from the center of the sphere. So we're gonna do eight minus 2.55 giving us 5.45 centimeters to the left of the center of the sphere. Wonderful. So let me go ahead and change colors real quick and let us go ahead and find our magnification factor. Well, our magnification factor is just going to be the negative of S prime divided by s what this gives us is negative negative 2.55 divided by seven giving us positive 0.36. So now we have found the position of the image as well as the magnification factor corresponding to our final answer. Choice of C. Thank you all so much for watching. I hope this video helped. We will see you all in the next one.