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If we consider a small object of length $b$ that is placed flat along the axis of a concave mirror, how will the image produced be different from the object?

I know that a lens will magnify or diminish an image, depending upon the position of the object with respect to the lens. However, that occurs only to the dimension normal to the axis of the lens.

Why should the image produced, in the case above with object of length $b$, be any different from the original object?

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  • $\begingroup$ Does your object have any thickness? $\endgroup$ – SchrodingersCat Oct 24 '15 at 11:49
  • $\begingroup$ @Aniket It doesn't. It only has a length along the axis. Nothing more. $\endgroup$ – Gummy bears Oct 24 '15 at 11:58
  • $\begingroup$ If it's got zero extent perpendicular to the optic axis, then all you have is the longitudinal compression, and all you can see in any 2-dimensional plane is a dot. No distortion is possible. $\endgroup$ – Carl Witthoft Oct 24 '15 at 21:08
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As there is a specific length to the object (b), let us call this object a stick. Let us imagine that this stick is made of infinitely many point objects (dots) placed on the axis of the mirror. Which implies that the distance between the first dot and the last dot on the stick is b. We can calculate where each dot forms its image. To know the change in length, just calculate the images of the first dot and the last dot on the stick and the distance between these image dots gives the length of the image stick. But, this only works when none of the dots on the stick is at focus of the mirror. If any one of the dots is at focus, it is trivial that the image stick is distorted.

Basically, the first and last points of the image stick need not be separated by the same distance as of the object stick.

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  • $\begingroup$ This is unclear, and does not appear to describe distortion. If each point on $b$ is mapped from $y_j$ to image height $Y_k$ linearly, then you have pure magnification. It's only because (for simple lenses, etc) the mapping is nonlinear that you get distortion. $\endgroup$ – Carl Witthoft Oct 24 '15 at 21:06
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    $\begingroup$ @Carl, I guess you are describing distortion for an object perpendicular to the optic axis. Then yes, that's how it is. It's also true that we only have length contraction or expansion for an object with no height (perpendicular to the axis) and we do not call this distortion. I should have written change in length rather than distortion. Anyway, I was answering the question " Why should the image produced, in the case above with object of length (b) be any different from the original object?" Thanks for the correction. $\endgroup$ – Madhav Oct 25 '15 at 1:46

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