Reflection and Mirrors Legacy Problem #23 Guided Solution

In this problem, a spherical mirror is used to create an upright image of the patient's tooth. The tooth becomes the object, and it has a distance of 1.8 centimeters. That's D0. The magnification of the image is 4.5, which means that the image is 4.5 times bigger than the object itself. That's probably the reason for the mirror. Now what we're asked in the first part of the question is, what type of mirror, concave or convex, is being used? No calculation here, just a simple understanding of the concepts. One of the concepts is that when you use a convex mirror to produce an upright or virtual image, the image is always reduced in size. When you use a concave mirror to produce an upright or virtual image, the image is magnified in size. So since this image is magnified by a factor of 4.5, we know that we must have a concave mirror here. Now the second part of the question is, what is the focal length? Finding the focal length means we must first have the image distance and the object distance. Now the object distance is easy. It's 1.8 centimeters. To find the image distance, I'll have to use the idea that the magnification is 4.5. To say that magnification is 4.5 means that the high to whole ratio is 4.5. And that 4.5 is equal to the negative die per doe ratio. And so I can say 4.5 equals the negative of die divided by the 1.8 centimeters for doe. And I can rearrange that to solve for die. And I end up getting a value for die of negative 8.1 centimeters. The negative indicates that I have a virtual image. Now I can use the mirror equation in order to find the focal length. I go 1 over F equals 1 over doe, which is 1.8, plus 1 over die, which is negative 8.1. When I evaluate the right side of the equation, I get as a value 0.43210. That's 1 over focal length. So I take the reciprocal of that number, I'll get the focal length. And it comes out to be 2.3143 centimeters. And I can round that to two significant digits, such that it's 2.3 centimeters.