Question

Write down some important conclusions from the sign convention for spherical mirrors.

Answer 1

The sign convention is also known as the new Cartesian sign convention.

The following diagram shows the sign convention.

1. The height of the object is taken as positive (+ve) if the object lies above the principal axis. Height is negative (-ve) if the height lies below the principal axis.
2. Distance of the object ‘u’ is always taken in negative sign (-ve) as it is kept on the left side of the mirror.
3. In the case of image distance ‘v’ the sign is negative (-ve) if the image is formed in front of the mirror and it is positive (+ve) if the image is formed at the back of the mirror.
4. In the case of a convex mirror, the ‘v’ value is always positive (+ve) because the image always forms behind the mirror.
5. As ‘u’ is always negative the mirror formula can be obtained as

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

Where ‘v’ is denoted as image distance, ‘u’ is denoted as object distance and ‘f’ is denoted as focal length.