An object 0.600 cm tall is placed 16.5 cm to the left of the vertex of a concave spherical mirror having a radius of curvature of 22.0 cm. (b) Determine the position, size, orientation, and nature (real or virtual) of the

Video transcript

Welcome back, everyone. We are making observations about a grasshopper that is sitting to the left side of a concave spherical mirror. We're told that the grasshopper has a height of one centimeter and it sits 14 centimeters to the left of the concave spherical mirror. Now, the magnitude for the radius of curvature is centimeters, which means we can find its focal point by R over two, which is 10 centimeters. And we are tasked with finding what is the position of the image, what is going to be the size of the image? And then to further classify any characteristics of the image. Let's go ahead and start with S prime here. We actually have an equation that relates the position of the object position of the image and the focal point given as follows one over S plus one over S prime is equal to one over f rearranging our equation a little bit. We get that one over S prime is equal to one over F minus one over S which means solving for S prime gives us S F divided by S minus F which let's go ahead and calculate that we have 14 times 10 divided by 14 minus 10, which gives us positive 35 centimeters, which means 35 centimeters to the left of our spherical mirror changing colors here. Let's go ahead and find the height or the size of our image. Well, the size of our image is just gonna be given by the magnification factor times the height of our object. But what is our magnification factor? And my apologies is actually going to be the absolute value of the magnification factor times the height of our object. But what is our magnification factor? So that's just going to be the negative of S prime divided by S. So this is negative 35 divided by 14 giving us negative 2.5. So that means the size of our image is going to be the absolute value of negative 2.5 times one centimeter which just gives us 2.5 centimeters. Now let's go ahead and specify some characteristics here about our image. If you look the position of our image is greater than zero, meaning that our image would be considered real. And we have that our magnification factor is less than zero, meaning that our image is inverted. So we have found the position of our image, the size of our image and classified some characteristics about our image which all correspond 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.