Sign Convention for the Parameters Related to the Mirror Equation:

The mirror equation is a fundamental equation in optics that relates the object distance (p), the image distance (q), and the focal length (f) of a mirror. To understand the sign convention for these parameters, let's break it down into different sections:

1. Object Distance (p):
The object distance (p) is the distance between the object and the mirror. It can be positive or negative depending on the position of the object relative to the mirror.

- When the object is placed in front of the mirror (real object), the object distance is considered positive.
- When the object is placed behind the mirror (virtual object), the object distance is considered negative.

2. Image Distance (q):
The image distance (q) is the distance between the image and the mirror. It can also be positive or negative depending on the position of the image relative to the mirror.

- When the image is formed in front of the mirror (real image), the image distance is considered positive.
- When the image is formed behind the mirror (virtual image), the image distance is considered negative.

3. Focal Length (f):
The focal length (f) is a property of the mirror and represents the distance between the mirror and its focal point. It can be positive or negative depending on the type of mirror.

- For a concave mirror (converging mirror), the focal length is considered positive.
- For a convex mirror (diverging mirror), the focal length is considered negative.

Summary of Sign Convention:
To summarize the sign convention for the mirror equation parameters:

- Object distance (p):
- Positive for a real object (in front of the mirror).
- Negative for a virtual object (behind the mirror).

- Image distance (q):
- Positive for a real image (in front of the mirror).
- Negative for a virtual image (behind the mirror).

- Focal length (f):
- Positive for a concave mirror (converging mirror).
- Negative for a convex mirror (diverging mirror).

Importance of Sign Convention:
The sign convention is essential in correctly applying the mirror equation to solve problems in optics. By following the sign convention, we can determine the nature (real or virtual) and the position (in front or behind the mirror) of the object and image formed by the mirror.

Example:
Let's consider an example using the sign convention:
For a concave mirror with a focal length of +10 cm, if the object distance is +20 cm, we can determine the image distance using the mirror equation:

1/f = 1/p + 1/q

1/10 = 1/20 + 1/q

By solving this equation, we can find the image distance (q) and determine the nature and position of the image formed.

In conclusion, the sign convention for the parameters related to the mirror equation is crucial in optics to determine the nature and position of the object and image formed by the mirror. By following the sign convention, we can solve problems accurately and understand the behavior of light rays in reflection.

1) all distance to be measured from the pole2) the distance is measured in the direction of incident light to be taken positive and those measured in the direction opposite to incident light to be taken negative