Cartesian Sign Convention

In the scenario where the choice of the sign is arbitrary, a sign convention is a selection of the actual interpretation of signs for a system of values. A sign convention must be specified, comprehended, and adhered to. In this article, the Cartesian sign convention will be discussed. 

The origin of the Cartesian coordinate system is located at the optical component’s centre. Normal to the optic axis distances are positive above and negative below. We indicate object space distances as l, h, and f, and image space distances as l’, h’, and f’. Acute angles are positive when rotated anticlockwise from the optic axis and negative when rotated clockwise.

What is the Cartesian Sign Convention? 

The Cartesian sign standard for light refraction by a lens. The optical centre O of the lens serves as the origin when the primary axis of the lens serves as the coordinate system’s x-axis. The item is always placed on the left side of the lens. All distances parallel to the primary axis are calculated from the lens’s optical centre.

For spherical lenses, a new Cartesian Sign Convention has been developed:

•  Distances calculated in the incoming light’s opposite direction are regarded as negative distances. 
• Positive distances can be referred to as those measured perpendicular and upward to the primary axis.
•  Negative values can be assigned to distances that are measured perpendicular and downhill to the primary axis.

Sign Conventions For Lenses

For Concave Lenses:

• Because the object is continually put in front of the mirror, its sign is interpreted as negative.
• Because the concave centre of the convex mirror’s curvature and the focus are in front of it, the signs of the radius of curvature and focal length are interpreted as negative.
• When an image is produced in front of a mirror, the distance between the image and the mirror is – (negative), and when an image is generated behind a mirror, the distance between the image and the mirror is + (positive).
• When talking about the erect picture, total height is always positive; whereas, in the case of the inverted image, the height is negative.

For Convex Lenses:

• Because the article is continually put before the mirror, its sign is interpreted as negative.
•  Because the centre of the convex mirror’s curvature and the focus are behind it, the sign of the radius of curvature and distance during this case is + (positive).
•  When employing a convex lens, the image is usually created behind the mirror, hence the image distance is often positive. 
• Because a convex lens always produces an upright picture, the peak of the image is thought to be positive.

Sign Conventions For Mirrors

 In the case of a spherical mirror, 

• all signs are taken from the pole, which is commonly referred to as the origin.
•  The height is measured in terms of + (positive) above the primary axis and − (negative) below the principal axis.

In The Case Of Convex Mirror

• Since the item is constantly in the front part of the mirror, the distance of the object is always negative.
• Since the mirror of the concave centre of the curvature and the focus are in the front of it, the curvature’s radius and the focal length are represented as negative here.
• When any image is produced in the mirror, the total distance between the mirror and image is generally negative. On the other hand, when the image is generated behind the mirror, the total distance between the mirror and the image is always positive.
• Since the item is always situated in front of the mirror, the object distance is considered negative in the case of a convex mirror.

In Case Of A Convex Mirror

•  The curvature’s radius and the focal length are always positive because the centre of curvature and focus are behind it.
• When using a convex mirror, the picture is always created behind the mirror, hence the image distance is always positive.
• Because a convex mirror always produces an upright picture, the image height is regarded as positive.

Conclusion

In the case of convex mirror object distance, focal length, the radius of curvature is negative. The distance between image and mirror when behind the object is positive and when the same is in the front it is negative. In the case of concave mirror object distance, focal length, the radius of curvature is always positive. Image height is regarded as positive as is  Produces upright image. 

In the case of concave lens object distance, centre of curvature and focus are positive. Also, image distance when the image is in front is negative and when the same is behind it is positive. In the case of a convex lens, the object distance is negative as it is placed before the mirror. Also, image distance as the image is often upright is positive.