Sorry if this is a stupid question, I only have an elementary understanding of physics. When a light ray that isn't parallel to the principal axis or passes through the focal point hits the surface of a concave mirror? In my high school and lower division college physics classes, we've only been taught what happens when the light rays coming off of an object fit either one of those descriptions. Just curious.
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$\begingroup$ You might get a good understanding of light from watching these Optical Puzzles videos from 3blue1brown. $\endgroup$– mmesser314Commented Nov 16 at 15:06
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$\begingroup$ Were you taught that "angle of incidence equals angle of reflection?" The angle, in the case of the curved mirror, is the angle between the ray and the plane that is tangent to the mirror at the exact point where the ray hits the mirror. $\endgroup$– Solomon SlowCommented Nov 16 at 15:09
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$\begingroup$ See this diagram. Rays originating from the same point on the object will hit the same point in the image; we just use a parallel ray and a ray that goes through the focus to find the location of that point. $\endgroup$– Filip MilovanovićCommented Nov 16 at 17:32
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2 Answers
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For the conditions you mentioned, light rays parallel to the principal axis converge at the axis. Keep in mind that this is taking the paraxial approximation; more on that can be found via Wikipedia; it's a very well-known approximation based on the fact that the radius of curvature is very large as compared to the aperture of your mirror.
For any general case, you will need a variety of parameters to be understood, such as: the focal length of the optical instrument under study, initial positions of objects and their nature, and the final location of object. Equations are used for a mirror and a lens (separately for both), and with them comes along the entire section of optics.
For the wave nature of light and its dispersion, you might need to study various experiments such as Young’s double-slit experiment and Fraunhofer diffraction, Huygens wave theory, Newton's rings, plus nodal behaviour.
You can check out optics textbooks for undergraduate courses. I can recommend Born and Wolf. Keep in mind that optics is a very vast topic.
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It reflects. Remember that a basic property of reflection is that the angle of incidence is equal to the angle of reflection. The light ray hits the concave mirror at some angle, and is reflected at the same angle. Of course, the incoming angle varies across the mirror depending on where exactly the point of contact is.
The reason we focus on parallel light rays or rays that pass through the focus is that those are the easiest to calculate, but you can get the path of every other light ray from first principles above.
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$\begingroup$ Re, "...parallel light rays...through the focus..." Assuming that there even is a focus ("concave" covers more territory than "ellipsoidal or parabolic,") then another big part of why we are interested in rays that are (close to) parallel to the mirror's optical axis and whose reflection passes through (or close to) the focal point is that those mirrors form real images. $\endgroup$ Commented Nov 16 at 17:55