Solving Mirror Questions: Formula & Examples

[Kdawg]

I have a few mirror questions. I missed class and didnt get the formulas to do these. If some one could help me out it would be appriciated. The formulas I have in my notes are 1/f = 1/do + 1/di and hi = (ho * di) / do. I don't think I have enough info to use these formulas and I am guessinf there is a formula or two I am missing.

1.)A dentist uses a small mirror of radius 55 mm to locate a cavity in a patient's tooth. If the mirror is concave and is held 10 mm from the tooth, what is the magnification of the resulting image?

2.)A production line inspector wants a mirror that produces an upright image within magnification of 7.0 when it is located 18.0 mm from a machine part.
What is its radius of curvature?

3.)Shiny lawn spheres placed on pedestals are convex mirrors. One such sphere has a diameter of 48 cm. A 12 cm robin sits in a tree 2.3 m from the sphere. Where is the image of the robin? How long is the robin's image?

4.)The image of the moon is formed by a concave mirror whose radius of curvature is 4.41 m at a time when the moon's distance is 3.80 105 km. What is the diameter of the image if the diameter of the moon is 3480 km?

5.)A shaving mirror has a radius of curvature of 33.0 cm. When a face is 11.0 cm away from the mirror, what is the magnification of the mirror?

 

[SpaceTiger]

You really should show your work when posting here. For standard mirror equations, you'll need to do a web search.

 

[thepatientmental]

Hello there,

I would be happy to assist you with solving these mirror questions. The two formulas you have in your notes, 1/f = 1/do + 1/di and hi = (ho * di) / do, are indeed the correct formulas to use for these types of problems. However, it is important to note that there may be additional information or assumptions needed in order to solve the problem accurately.

1. To solve this problem, we can use the formula 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. We are given the radius of the mirror, which is half of the focal length, so we can calculate f = 55 mm / 2 = 27.5 mm. We are also given the object distance, which is 10 mm. Plugging these values into the formula, we get 1/27.5 = 1/10 + 1/di. Solving for di, we get di = 6.875 mm. To find the magnification, we can use the formula hi = (ho * di) / do, where ho is the object height and hi is the image height. Since the mirror is small, we can assume that ho is approximately equal to the size of the cavity, which is not given in the problem. Therefore, we cannot solve for the magnification without this information.

2. For this problem, we can use the formula hi = (ho * di) / do to solve for the magnification. We are given the magnification, which is 7.0, and the object distance, which is 18.0 mm. However, we are not given the object height, so we cannot solve for the image height or the radius of curvature without this information.

3. This problem involves a convex mirror, so we will use the formula hi = (ho * di) / do to solve for the image distance. We are given the diameter of the mirror, which is 48 cm, so we can find the focal length, which is half of the radius of curvature. Therefore, f = 24 cm. We are also given the object distance, which is 2.3 m. Plugging these values into the formula, we get hi = (12 cm * 2.3 m) / 24 cm = 1.15 m