A spherical, concave shaving mirror has a radius of curvature of 32.0 cm. (b) Where is the ? Is the real or virtual?

Video transcript

Welcome back. Everyone. We are told that a very small round object is placed three centimeters away from a concave mirror. And we are told that the radius of curvature for the mirror is nine centimeters. And we are tasked with finding what is going to be the distance of the image away from the mirror vertex. And whether or not the image is virtual. Well, since we were given the radius of curvature, we can go ahead and find our focal point. Our focal point is simply given by the radius divided by two, which gives us 4.5 centimeters. Now, we have a relationship between the position of the object position of the image and the focal point 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. And solving for S prime, we get S F divided by S minus F, we have all of these values. So let's go ahead and calculate this. What we get for the image distance is three times 4.5 divided by three minus 4.5. What this gives us is negatives nine centimeters or nine centimeters to the right, right now, what about it being virtual? Well, since we have the object of or sorry, rather the image distance is less than zero, we have that our image is indeed virtual. So we found not only the position of the image but the fact that it is virtual which corresponds to our answer. choice of D Thank you all so much for watching. I hope this video helped we will see you all in the next one.