Calculating Di and Hi for Lawn Sphere Mirror Problem

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To solve the lawn sphere mirror problem, first determine the focal length using the diameter of the sphere, which is 40 cm, leading to a radius of curvature of 20 cm. The focal length for a convex mirror is positive and can be calculated as half the radius of curvature. Once the focal length is known, use the mirror equation 1/f = 1/di + 1/do to find the image distance (di), where the object distance (do) is 150 cm (1.5 m). Finally, apply the magnification formula hi/ho = -di/do to find the height of the robin's image. The calculations will yield the location and size of the robin's image.
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Homework Statement


Lawn spheres placed on pedestals are convex mirrors. One such sphere has a diameter of 40.cm. A 12 cm robin sits in a tree 1.5m from the sphere. Make a representative sketch. Where is the image of the robin? How long is the robins image?


Homework Equations


1/f=1/di+1/do
hi/ho=-di/do



The Attempt at a Solution


I have a diagram but am stuck on where to go from here?
 
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Hello Capri,

Welcome to Physics Forums! :smile:

First, work your way to finding the focal length of the mirror.

You know the diameter of the sphere. From that, you can determine the radius of curvature*. From there you should be able to look up some formula for the focal length as a function of the radius of curvature. Oh, and don't forget to pay attention to the +/- sign and how that relates to concave or convex mirrors.

*[Edit: radius of curvature is often called center of curvature.]
 
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