A point object is placed at the centre of curvature of a spherical concave mirror. Which one among the following would be the correct location of image formed?
- (a)At infinity
- (b)At the centre of curvature
- (c)At the focal point
- (d)Between the focal point and the centre of curvature
Correct — B, at the centre of curvature. For a concave mirror, when the object is placed exactly at the centre of curvature (C), the reflected rays meet again at C, forming a real, inverted image of the SAME size as the object, right at the centre of curvature. This follows from the mirror formula with u = 2f, which gives v = 2f.
- (a)At infinity — The image forms at infinity only when the object is placed at the FOCUS (F) of the concave mirror, not at the centre of curvature.
- (c)At the focal point — A real image forms at the focus (F) when the object is at INFINITY (parallel rays), not when it is at C.
- (d)Between the focal point and the centre of curvature — The image lies between F and C only when the object is placed BEYOND the centre of curvature; for an object exactly at C the image is at C itself.
A concave (converging) mirror has its centre of curvature C at a distance R (the radius) and its focus F at R/2, so C = 2F. Where the image forms, and its nature, depend on where the object sits relative to F and C. Using the mirror formula 1/v + 1/u = 1/f with u = 2f gives v = 2f — the image at C.
Learn the standard object-position table for a concave mirror. Object at C is the special 'same-size' case: image at C, real, inverted, magnification 1. The three distractors are the images for the neighbouring object positions (at F -> image at infinity; at infinity -> image at F; beyond C -> image between F and C).
- Concave mirror: the centre of curvature C is at twice the focal length (R = 2f).
- Object at C -> image at C: real, inverted, same size (magnification = 1).
- Object at F -> image at infinity; object at infinity -> image at F.
- Object beyond C -> image between F and C (real, inverted, diminished).
With the object at C, the image forms back at C — the same-size case (option B).
- Swapping the 'object at F -> image at infinity' and 'object at infinity -> image at F' cases.
- Forgetting that at C the image is the same size (magnification exactly 1).
Asked as 'where is the image when the object is at C/F/beyond C' or via the mirror formula in a numerical.
No directly related past PYQ was found.
- practice — not a real PYQ
For a concave mirror, the image is real, inverted and of the same size as the object when the object is placed
- (a)at the focus
- (b)between focus and pole
- (c)at the centre of curvature
- (d)at infinity
Answer(c) at the centre of curvature — image at C, same size.
- practice — not a real PYQ
A concave mirror forms a highly diminished, real image at its focus when the object is
- (a)at C
- (b)at F
- (c)at infinity
- (d)between P and F
Answer(c) at infinity — parallel rays converge to the focus.