What is the spherical mirror formula? Also, write down the sign conventions for the spherical mirror formula.

The spherical mirror formula relates the focal length $f$, the object distance $u$, and the image distance $v$ for a spherical mirror (concave or convex mirror). The formula is given as:

1/f=1/v+1/υ​

Definitions:

• f: Focal length of the mirror
• v: Image distance (distance from the mirror to the image)
• υ: Object distance (distance from the mirror to the object)

Sign Conventions for Spherical Mirrors:

In the context of spherical mirrors, the following sign conventions apply:

1. Object Distance (υ):

   • For real objects,  is negative (since the object is in front of the mirror).
   • For virtual objects, υ is positive.

2. Image Distance ($v$):

   • For real images (formed on the same side as the object), v is positive.
   • For virtual images (formed on the opposite side of the object), $v$ is negative.

3. Focal Length ($f$):

   • For concave mirrors (converging mirrors), f is positive.
   • For convex mirrors (diverging mirrors), f is negative.

4. Radius of Curvature (R):

   • The radius of curvature for the mirror is positive for concave mirrors and negative for convex mirrors. The focal length is related to the radius of curvature by the equation f=R/2

5. Mirror Type:

   • Concave Mirror: Converging mirror, used to form real or virtual images.
   • Convex Mirror: Diverging mirror, always forms virtual images.

These sign conventions help maintain consistency in calculations for spherical mirrors.