A 5.00-cm object is placed 30.0 cm away from a convex mirror with a focal length of -10.0 cm.

step 1 So in this question, we have given height of the object H .O. equals to 5 .00 cm and object is p

A 5.00-cm object is placed 30.0 cm away from a convex...

Key Concepts

Mirror Equation

The mirror equation, 1/f = 1/do + 1/di, is fundamental in geometrical optics. It relates the focal length (f), the object distance (do), and the image distance (di) of a mirror. This equation provides a method to determine the location of the image formed by reflecting surfaces and is applicable to both concave and convex mirrors, provided that the appropriate sign conventions are used.

Magnification

Magnification is given by the formula m = -di/do and indicates the ratio of the height of the image to the height of the object. It also determines the image's orientation: a positive magnification means the image is upright, while a negative magnification means the image is inverted. Additionally, the absolute value of the magnification indicates the relative size difference between the image and object.

Virtual Images

A virtual image is formed when the reflected light rays diverge, such that their extensions appear to originate from a common point behind the mirror. Virtual images cannot be projected onto a screen because they are not formed by actual light convergence. In the context of convex mirrors, the images are always virtual, appearing smaller and upright relative to the object.

Convex Mirrors

Convex mirrors have outwardly curving surfaces, which always cause the reflected rays to diverge. This results in images that are diminished in size, always upright, and situated behind the mirror. The nature of convex mirrors makes them useful in applications where a wide field of view is required, such as in vehicle side mirrors and security mirrors.

Sign Conventions

Sign conventions in optics are critical for correctly applying the mirror and lens equations. For mirrors, distances measured in the direction of the incoming light are generally considered positive, while distances measured against it are negative. For convex mirrors, specifically, the focal length is taken as negative because the mirror’s curvature causes the focal point to be virtual and located behind the mirror surface.