( In this blog, Notation p and q are used for the Object distance and image distance respectively, You Can use your own notation like u and v or other notation, depending on the notation used in your textbook.) 

New Cartesian Sign Convention Rules for the Object placed  in front of spherical mirrors (Concave or Convex) with the pole as an Origin and Principal Axis as an X-Axis are as follows:

  1. The object is always placed to the left of the mirror. It means that the light from the object falls on the mirror from the left-hand side.
  2. All the distances are measured from the pole of spherical mirrors.
  3. All the distances measured parallel to the principal axis on the left (front) side (against the incident light) are taken with a negative (-ve) sign.
  4. All the distances measured parallel to the principal axis Right side (behind) of the mirror ( ie. in the same direction of incident light) of the mirror are taken with a Positive (+ve) sign.
  5. All the distances measured perpendicular and above to principal axis i.e. the erect images are taken as positive (+ve) and below i.e. inverted image is taken as negative (-ve).

Sign convention for Concave Mirror (Converging):

  1. Distance of object from the mirror: As the Object is always placed to the left (front) of the mirror so, the object distance is taken always as negative (–ve).
  2. The radius of curvature (R) and focal length (f): The center of curvature and focus lie in the left (front) of the concave mirror, so the radius of curvature (R) and focal length (f) of the Concave Mirror are always taken as negative (-ve) 
  3. Distance of image from a mirror: When an image is formed on the left side (front) of the concave mirror, the image distance is taken as negative (–ve) and when the image is formed Right side (behind) of the mirror, the distance of image is taken as positive (+ve).
  4. Height of the image: The height of the image is taken as positive (+ ve) in the case of an erect image (above the principal axis) and taken as negative (- ve) in the case of an inverted image (below the principal axis).


 
Example: Let an object 10 cm to the left of a converging mirror (Concave) of focal length 5 cm.
  1. In this case, the object distance p is negative (-ve), as it is to the left of the "origin" of the mirror
  2. The focal length f of the mirror is negative (-ve).
  3. The image is formed 10 cm to the left of the Mirror. This means that the image is real and, its (image) distance q is negative (-ve).
  4. The Object height h₀áµ¢ is Positive (+ve)  and Image height háµ¢ is Negative (-ve)




Sign conversion for Convex Mirror (Diverging):

  1. Distance of object from the mirror: As the Object is always placed to the left side (front) of the mirror so, the object distance is taken always as negative (–ve).
  2. The radius of curvature (R) and focal length (f): The center of curvature and focus lies right side (behind) the convex mirror, so the radius of curvature (R) and focal length (f) of the Convex Mirror is always taken as Positive (+ ve) 
  3. Distance of image from a mirror: As only the virtual image is formed right side (behind) the convex mirror, the distance of the image is always taken as positive (+ve).
  4. Height of the image: The height of the image is taken as positive (+ve) in the case of an erect image (above the principal axis) and taken as negative(-ve)  in the case of an inverted image (below the principal axis).


 
Example: Let an object 10 cm to the left of a diverging mirror (Convex) of focal length 5 cm.
  1. In this case, the object distance p is negative (-ve), as it is to the left of the "origin" of the mirror
  2. The focal length f of the mirror is Positive (+ve).
  3. The image is formed 3.3 cm to the right of the Mirror. This means that the image is virtual and image distance q is positive (+ve).
  4. The Object height h₀ is Positive (+ve)  and the Image height háµ¢ is Positive (+ve) because both are above the principal axis.





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