How Do Double Concave Mirrors Create a Floating Image?

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SUMMARY

The discussion centers on the optical phenomenon created by a double concave mirror setup, consisting of two spherical concave mirrors with identical radii of curvature and focal lengths. When an object is placed at the center of the bottom mirror, light emitted from it reflects off the top mirror, which has a central hole, creating a floating image above this hole. The light reflects parallel from the top mirror and subsequently converges through the focal point of the bottom mirror, resulting in the observed image. This setup effectively demonstrates principles of optics and reflection.

PREREQUISITES
  • Understanding of spherical concave mirrors
  • Knowledge of focal length and radius of curvature
  • Basic principles of light reflection
  • Familiarity with optical diagrams and ray tracing
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  • Research the principles of ray optics and reflection in concave mirrors
  • Explore the mathematical relationships involving focal length and image formation
  • Study optical devices that utilize similar mirror configurations
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Students of physics, optical engineers, and anyone interested in the practical applications of concave mirrors in creating visual effects and images.

mrjeffy321
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I am trying to figure out how those double concave mirror set ups work to create an image above the mirror.
Does anyone know what I am talking about?

You have 2 [spherical] concave mirrors, both with the same radius of curvature (and thus the same focal length), one facing up, and the other facing down on top of the first. The mirror on top has a hole cut out of its center.
When you place an object in the center of the bottom mirror, an image of that object appears hovering in mid air over the hole cut in the top mirror.
If you need more clarification, see attached picture (the black square is the object, the gray square is the image).


Here is how I think it works, let's see if I am correct.
Since the mirrors have the same radius of curvature, then have the same focal length. Let's just say that the focal length just happens to be the distance between the ceneter of the top mirror and the center of the bottom mirror. So any object placed in the center of the bottom mirror emmits light that is relected (from the focal point of the top mirror) parallel of the top mirror. The the parallel light from the top is relected through the focal point of the bottom mirror (which is the center of the top mirror) and thus creates an image.
I further illustrated my idea on the attached image (the black lines emminating from the object bounce off the top mirror and are then shown by the green lines, which bounce off the bottom mirror, which then are shown by the blue lines becomming the image we see)
 

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