You hold a spherical salad bowl 60 cm in front of your face with the bottom of the bowl facing you. The bowl is made of polished metal with a 35-cm radius of curvature. (a) Where is the of your 5.0-cm-tall nose located?

Video transcript

Welcome back, everyone. We are making observations about a shot in a shot put competition which is a metal spherical ball. We are told that the diameter of this shot is 12 centimeters and we are told that it is placed centimeters away from a cup placed on the bench. Now, the spherical ball is going to act like a convex mirror. And we are tasked with finding what is going to be the position of the cup's image. Well, since we have the diameter, we can find the radius of curvature to be the negative of the diameter divided by two, which gives us negative six centimeters. And since we found the radius of curvature, we can find the focal point which is the radius divided by two, giving us negative three centimeters. Now, we have this relationship between the position of the object image and the focal point. We have one over S plus one over S prime is equal to one over f rearranging the equation a little bit, we can get one over S prime is equal to one over F minus one over S. And then solving for the position of our image, we get S F divided by S minus F. Let's go ahead and plug in our values here. We have that. This is equal to 20 times negative three, divided by 20 minus negative three, which gives us negative 2.61 centimeters or 2.61 centimeters to the right corresponding to our final answer. Choice of a Thank you all so much for watching. I hope this video helped. We will see you all in the next one.