The thin glass shell shown in Fig. E34.15 has a spherical shape with a radius of curvature of 12.0 cm, and both of its surfaces can act as mirrors. A seed 3.30 mm high is placed 15.0 cm from the center of the mirror along the optic axis, as shown in the figure.

(a) Calculate the location and height of the

of this seed.

Video transcript

Welcome back, everyone. We are making observations about an ant that has a height of 0.5 millimeters. Now, we are told that it is situated along the principal axis of a thin spherical shell of quartz coated with aluminum. Now this is going to act like a concave mirror. Now, we are told that the ant is seven centimeters away from the mirror's vertex. And we are told that the shell has a radius of eight centimeters. And what this means is that we have a focal length of the radius divided by two, which is four centimeters. We are tasked with finding two things. One, what is going to be the position of our image and two, what is going to be the height of our image? Let's start off with part one here. What can we say? Well, we have the following equality one over S plus one over S prime is equal to one over F where S represents the position of our object S prime represents the position of the image and F equals our focal length rearranging our equation here. What we get is one over S prime is equal to one over F minus one over s flipping both sides of our equation here. And combining the right hand side of our equation into one fraction. We get that S prime is equal to seven, which is SS times four, which is F divided by seven minus four. And what this gives us is positive 9.3 centimeters which means we are 9.3 centimeters to the left of the vertex for the position of our image changing colors here. Now let's move on to part two to find the height of our image. Well, the height of our image is just going to be equal to our magnification constant times the height of our option object. Now the magnification constant is found by the negative of the height of our image divided by the height of our object. What this gives us is negative 9.3 divided by seven which gives us negative 1.33. So now finding the height of the image, what we have is negative 1.33 times 0. millimeters giving us negative 0.67 millimeters which what this gives us since the image will be inverted is an image height of 0.67 millimeters. So now we have found both the position of the image and the height of the image which corresponds 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.