Calculating Di and Hi for Lawn Sphere Mirror Problem

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In summary, the problem at hand involves a convex mirror in the shape of a lawn sphere with a diameter of 40 cm. A robin with a height of 12 cm is situated 1.5 m away from the sphere. Using the equations 1/f = 1/di + 1/do and hi/ho = -di/do, one can determine the focal length of the mirror by calculating the radius of curvature. From there, the position and size of the image of the robin can be determined.
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Capri
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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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1. How do I calculate the diameter (Di) for a lawn sphere mirror?

To calculate the diameter of a lawn sphere mirror, you can use the formula Di = 2 x (Hi x tan(90/N)), where N is the number of mirror segments. This formula takes into account the height (Hi) of the mirror and the number of segments to determine the appropriate diameter for optimal reflection.

2. What is the purpose of calculating Di and Hi for a lawn sphere mirror?

The purpose of calculating Di and Hi is to ensure that the lawn sphere mirror is properly sized for optimal reflection. This involves finding the right balance between the height and diameter of the mirror to achieve the desired reflection angle and focal point.

3. Can I use a different formula to calculate Di and Hi for a lawn sphere mirror?

While the formula mentioned above is commonly used, there are other formulas that can be used to calculate Di and Hi for a lawn sphere mirror. Some may take into account additional factors such as the curvature of the mirror or the distance from the focal point. It is important to choose a formula that is appropriate for your specific needs and desired outcome.

4. How do I determine the number of mirror segments needed for my lawn sphere mirror?

The number of mirror segments needed for a lawn sphere mirror will depend on the desired level of reflection and the size of the mirror. Generally, the more mirror segments used, the more accurately the mirror will reflect light. However, too many segments may be difficult to manage and increase the chances of distortion. It is recommended to start with a smaller number of segments and adjust as needed.

5. Are there any online tools or resources available for calculating Di and Hi for a lawn sphere mirror?

Yes, there are various online tools and resources available for calculating Di and Hi for a lawn sphere mirror. These can range from simple calculators to more advanced simulation programs. It is important to choose a reliable and accurate tool that takes into account all relevant factors for your specific mirror design.

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