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Image formation for concave mirror when object is at centre of curvature

Physics Asked on May 14, 2021

Everywhere I see it is quoted that when an object is at C its reflected image by a concave mirror will also be at C (and be inverted and equal-sized), but when I draw it this is impossible, it always appears diminished and closer to the mirror than C. When I look close at pictures on the web they are never drawn accurately, for example, in the attached wiki image the focus clearly isn’t midway between the pole and the centre of curvature. Very confused! If somewhere could clarify it would be much appreciated.

enter image description here

One Answer

Think of the concave mirror as a parabola and the focus of the mirror as the focus of the parabola. Now from $2F$, draw an object of whatever height you want and draw a line parallel to the x-axis, namely $OA$. Wherever this line intersects the parabola say $A$, draw a line from this point and the focus and name this line $AF$. Draw another line passing from the object passing through the focus, $OF$. Wherever this line intersects the parabola, draw say $B$, draw a line from $B$ parallel to the X -axis and you'll get the image at the intersection of these lines which will be at a distance of $2F$ For an accurate image which you wanted you could refer to this : https://www.physicsclassroom.com/mmedia/optics/rdcmb.cfm

Answered by Sanika Khadkikar on May 14, 2021

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