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Hi Physics Stack Exchange Community. I am new to studying Optics. In my textbook there is constant mention of the images of objects placed at infinity for Concave, Convex Mirrors and Lenses. But it is unclear to me as to what is actually meant by saying so. Obviously it does not mean the object actually is placed at infinity which it cannot be whatsoever. My guess is this means that the object is placed at a large distance which is of a larger order than the aperture of the Mirror or Lens.

Am I right in thinking so? Can someone give mathematics based reasoning?

Paras Khosla
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Yes, you are right. This is a more geometrical problem than anything else. If a point object were placed closed to the mirror, you can imagine two light rays reaching the mirror from there (above and below the principle axis). Nowm if you drag that point object all the way back (further away from the mirror), the two light rays tend to point in the same direction, because the distance to the mirror is getting larger than the aperture of the mirror itself. This means that light rays can be approximated as coming from a very infinity with non-zero angular width.

There is no proof for this that the object will be at infinity. Unless we assume that $u$ (the object distance) is a really large number. So, in the focal length expression, $1/f= 1/v + 1/u$

$$1/u \to 0$$ because $u>>f$.

Our day to day life mirror apertures (and hence smaller focal lengths) are small compared to the distances we see ourselves in real life.

EDIT: Whatever assumptions here work well whether or not the mirror or the lens suffers from chromatic abberations (if you are learning CBSE, you might come to that point towards the end - each color depending on their refractive indices - in the cases of lens only, fall off at different focal points. This is the region that the user Vincent was talking about). Rays coming from a distance greater than that of the aperture is considered the "infinity". This is the basic idea.

Karthik
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  • Is there a mathematical expression, maybe an inequality that links these quantities? – Paras Khosla Mar 08 '19 at 13:19
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    @ParasKhosla All the light rays reaching the optical system from an "object at infinity" are assumed to be parallel, though light rays from a real object a very large distance away are not exactly parallel. That is the mathematical (or geometrical) definition of an "object at infinity". – alephzero Mar 08 '19 at 13:31
  • Maybe you should be more precise "All the light rays reaching the optical system from a ponctual object at infinity are assumed to be parallel". An object can be at infinity and have a non 0 angular width. – Vincent Fraticelli Mar 08 '19 at 13:48
  • @VincentFraticelli Yes, I have just added this into my answer. – Karthik Mar 08 '19 at 14:22
  • @KV18 Shouldn't $1/u\to 0$ as $u\to \infty$? – Paras Khosla Mar 08 '19 at 14:58
  • @ParasKhosla Yes. Sorry, I have edit the answer properly. – Karthik Mar 08 '19 at 15:19
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For a finite but large distance object, the geometric image is not quite in the focal plane and the intersection with the focal plane is a non-point spot.

But, for a real instrument, the image of a point is not a point but a spot (because of the geometric aberrations) and the sensor of the device itself has a finite resolution.

As a result, the criterion depends on the instrument: a ponctual object is at infinity if the size of the spot in the focal plane is less than the resolution of the instrument. The better the quality of the instrument, the greater the opening will be and the more the infinity will be far.

For a bad quality camera, infinity can be one meter forward !

Vincent Fraticelli
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