Question

The image formed by a concave mirror is real, inverted and of the same size as the object. The position of the object will be:

• A. at the focus
• B. between the focus and centre of curvature
• C. at the centre of curvature
• D. beyond the centre of curvature

Hint:

For concave mirrors, when the object is at the centre of curvature, the image formed is real, inverted, and of the same size as the object.

Answer 1

The Correct Option is C

For a concave mirror, the nature of the image formed depends on the position of the object relative to the mirror. When the object is placed at the centre of curvature (denoted as \( C \)) of the concave mirror, several key properties of the image can be determined using the mirror equation and ray diagrams. \smallskip 1.
Object Position at Centre of Curvature: The centre of curvature is a point located at a distance \( R \) (the radius of curvature) from the mirror's pole. When the object is placed at this position, it lies exactly at the same distance from the mirror as the image that forms. This is a key characteristic of concave mirrors, where specific object placements yield images with unique properties. \smallskip 2.
Image Properties:


Real Image: In this case, the rays of light converge after reflecting off the concave mirror, forming a real image. The image is formed in front of the mirror and can be captured on a screen.

Inverted Image: Since the object is placed at the centre of curvature, the reflected rays meet at the same position on the opposite side of the mirror (inverted), resulting in an inverted image.

Same Size as Object: The distance of the object from the mirror is equal to the distance of the image from the mirror. This results in an image that is the same size as the object. The magnification \( m \) for this case is given by: \[ m = \frac{\text{Image Height}}{\text{Object Height}} = -1 \] This means the image is of the same size as the object but inverted.
\smallskip 3.
Ray Diagram: A ray diagram can be used to visually demonstrate the formation of the image. In this case, the incident rays parallel to the principal axis reflect off the mirror and converge at the centre of curvature, where the object and image are symmetrically placed. \smallskip In conclusion, when the object is positioned at the centre of curvature of a concave mirror, the image formed is real, inverted, and of the same size as the object, as both the object and the image lie at the same distance from the mirror.