Theory:

We will use a set of sign conventions called the New Cartesian Sign Convention when dealing with a light reflection by spherical mirrors. The mirror's pole (\(P\)) is used as the origin in this convention. The x-axis (\(X'X\)) of the coordinate system is taken as the principal axis of the mirror.
 
The following are the rules to be followed while using sign convention:
  • Always place the object to the left of the mirror. This indicates that the object's light strikes the mirror from the left side.
  • The mirror's pole is used to measure all distances parallel to the principal axis.
  • All distances to the right of the origin (along \(+ x-axis\)) are positive, while those to the left (along \(– x-axis\)) are negative.
  • Positive distances are measured perpendicular to and above the principal axis (along \(+ y-axis\)).
  • Negative values are assigned to distances measured perpendicular to and below the principal axis (along the \(–y-axis\)).
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Sign convention for spherical mirrors
  
The below table shows the sign convention,
  
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