Physics Asked by bluscape on December 27, 2020
I’m trying to measure the X and Y profiles of a round object using a single camera. The camera has a direct view of the object in the X profile but sees the Y profile of the object as a reflection on a mirror mounted at 45 degrees. The problem is that the Y profile seen by the camera is smaller than the X profile of the object. Although the object is round. See the attached diagram, photo of the setup and a photo from the camera.
I would think that the reflection of the Y profile will be the same distance from the camera as the X profile and therefore have the same size. But it does not.
Why is the Y profile smaller than the X profile?
Or why is the Y profile (reflection) further away from the camera?
I did get the mirror from my wife’s makeup so it could be that the reflective coating is at a radius. But the glass itself seems flat.
The way you have drawn your diagram suggests the mirror reflecting the y-profile is at the same distance from the camera as the object is. But the 'effective' distance to the y-profile image also needs to include the distance from the object to the mirror. See my adaption of your original sketch,
Correct answer by Penguino on December 27, 2020
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