What is the relationship if any between the object distance and image distance for concave mirror?

State the relationship between object distance, image distance, and focal length of a spherical mirror.

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Hint: A spherical mirror is a curved mirror created by a part of a hollow glass sphere. This sphere has a reflecting surface. The two types of spherical mirrors are the Concave mirror and Convex mirror. A concave mirror is a curved mirror with a reflecting surface on the hollow side. The convex mirror is a curved mirror having a reflecting surface on the outer side. The relationship between object distance, image distance, and focal length of a spherical mirror is known as the mirror formula.

Complete step by step answer:

Object distance:The distance between the object and the point of incidence on the mirror is referred to as the object distance. It is denoted as the letter of small ‘$u$’.Image distance:The image distance is the distance between the mirror's point of incidence and the point where the image is generated. It is denoted by the letter of small ‘$v$’.Focal length:The focal length is the distance between the pole and the focal point ($f$). A spherical mirror's focal length is then roughly half its radius of curvature. It is denoted by the letter ‘$f$’.Mirror formula is the relationship between object distance $(u)$, image distance $(v)$, and focal length $(f)$ is given by,$\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}$$f$ - Focal length of the spherical mirror(distance between the pole and the mirror's main objective)$u$ - Object distance(distance between the object and the pole)$v$ - Image distance (the distance between pole and image)

Here an object \[AB\] at a distance $u$ from the pole. The image $A'B'$ is formed at distance $v$ from the mirror. The position of the image is obtained by drawing an image and a ray diagram.

Additional information:

Convex lenses are also called converging lenses. The rays converge after passing through them, whereas concave lenses are called diverging lenses because the rays diverge after passing through them. These lenses can produce real or virtual images, depending on their distance from the lens, and they can also be of varying sizes. The image distance is computed using the lens formula and knowledge of the object distance and focal length. The Lens formula describes the relationship between the distance of an image I the distance of an object (o), and the focal length ($f$) of the lens in optics.

Note:

In everyday life, spherical mirrors are employed in a variety of ways.Dentists use concave mirrors to observe an enlarged image of a tooth.Concave mirrors are also utilized in the headlights of automobiles.Because convex mirrors improve the field of view, they are utilized as rear-view mirrors in automobiles.Because they diffuse light over a larger area, convex mirrors are utilized in street light reflectors.Solar cookers employ concave mirrors.As a result, spherical mirrors play a significant role in our daily lives. As a result, the spherical, mirror role would be very appreciated.