Concave and Convex Mirrors: Principal Focus

Spherical Mirrors

• Rays parallel to the principal axis, falling on a concave mirror, intersect at a point on the principal axis, called the principal focus (F).
• Rays parallel to the principal axis, reflected by a convex mirror, appear to come from a point on the principal axis, also called the principal focus (F).
• The distance between the pole and the principal focus of a spherical mirror is called the focal length (f).
• The reflecting surface of a spherical mirror is spherical, with a circular outline, and the diameter of the reflecting surface is called its aperture.
• For spherical mirrors of small apertures, the radius of curvature (R) is equal to twice the focal length (f), i.e., R = 2f.

Image Formation by Spherical Mirrors

• Image formation by a concave mirror can be located for different positions of the object.
• The images formed by a concave mirror can be real or virtual, enlarged, diminished, or have the same size.
• The focal length of a concave mirror can be determined by measuring the distance of the image from the mirror.

Image Formation by Concave Mirrors

• To obtain an erect image of an object using a concave mirror, the object should be placed within the focal length of the mirror.
• The image formed is virtual and erect, and smaller than the object.
• A ray diagram can be used to show the image formation in this case.

Types of Mirrors

• Concave mirrors are used in headlights of a car to produce a parallel beam of light.
• Convex mirrors are used in side/rear-view mirrors of a vehicle to provide a wide-angle view.
• Concave mirrors are used in solar furnaces to focus sunlight.

Convex Lenses

• One-half of a convex lens covered with a black paper can still produce a complete image of the object.
• The image formed by a convex lens can be real, inverted, and larger or smaller than the object, depending on the object's position and the lens's focal length.

Image Formation by Concave Lenses

• A concave lens of focal length 15 cm forms an image 10 cm from the lens, and the object is placed at a distance of 30 cm from the lens.
• A ray diagram can be used to show the image formation in this case.

Image Formation by Convex Mirrors

• An object placed at a distance of 10 cm from a convex mirror of focal length 15 cm forms a virtual image 6 cm from the mirror.
• The image is erect and smaller than the object.

Magnification

• The magnification produced by a plane mirror is +1, meaning the image is the same size as the object.
• The magnification produced by a convex mirror can be calculated using the formula: magnification = -f / (d - f), where d is the distance of the object from the mirror.