The Focal Length Of Convex Mirrors

A mirror is a reflective surface that reflects light and creates either a real or a virtual picture. When an object is placed in front of a mirror, the object’s image is reflected in the mirror. 

The object emits the incident rays, and the reflected rays generate the image.

• Plane Mirrors
• Spherical Mirrors

A plane mirror is a reflective surface that is flat and smooth. A spherical mirror has a constant curvature radius and a consistent curve. Spherical mirrors with painted inward surfaces are known as convex mirrors, whereas those with painted exterior surfaces are considered concave mirrors.

Before digging in, a few words like principal axis, the centre of curvature, the radius of curvature, principal focus, and focal length of the convex mirror are essential to understand.

Convex mirror

Unlike concave mirrors, this type of mirror has an outward curve. The images formed by the Convex mirror are erect, virtual, and diminished. The image size depends on the distance between the mirror and the object. When the beam of light strikes the surface, the lines get reflected by diverging or spreading out. For this reason, these mirrors are known as diverging mirrors. 

The focal length of a convex mirror

• When rays are coming from infinity and after reflection, they seem to meet at a point. This point is called the virtual focus of the mirror. P is the pole of a spherical mirror. The distance between the focus F and P is known as the focal length of the convex mirror and is denoted by (f). According to the paraxial approximation, the focal length of a convex mirror is half of its radius of curvature.
• The power of an optical element is given by the inverse of the focal length (1/f), and its unit is dioptre (1/m).

The centre of the curvature

The centre of the spherical surface of which the mirror is a part is called the centre of curvature C of the mirror. 

Principal axis

The line that passes from the mirror surface through the mirror’s centre of curvature is known as the principal axis.

Image formation rules

Rule 1: The incident ray comes parallel to the principal axis. Generates a reflected ray that appears to originate from the principal focus on the other side of the mirror.

Rule 2: If the incident ray of light appears to head towards the principal focus on the other side of a convex mirror, the reflected ray is parallel to the principal axis.

Rule 3: If the incident ray of light is not parallel or perpendicular to the principal axis and is heading straight for the pole of the convex mirror, then the rays reflected such that the reflected ray has an angle of reflection equal to the angle of incidence measured between the principal axis and each ray.

Rule 4: A ray of light heading towards the centre of curvature on the other side of the mirror gets reflected in such a way that it retraces its path.

Image formation by a convex mirror

The reflecting surface of convex mirrors is on the outside of the sphere, making the centre of curvature and the focal point on the other side of the mirror from the object. The focal length on the direction of incident light is taken as positive.

Conclusion

The focal length can be defined as the distance between the mirror and its principal focus. The focal length helps determine how sharply the apparatus converges or diverges the light. 

A concave mirror can be defined as a surface that is curved to the inside

The reflection mirror follows the law of reflection, which are as follows:

• The incident reflected, and regular rays lie in the same plane.
• The angle of reflection(r) is always equal to (i) incidence.