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Sign convention for Spherical Mirrors – class 10

Here we will present the New Cartesian Sign Convention for Spherical Mirrors for measuring various distances in the ray diagrams of spherical mirrors (convex mirrors and concave mirrors).

Also read this side by side Sign convention for spherical lenses

Sign convention for Spherical Mirrors

According to the New Cartesian Sign, the Sign Convention for spherical mirrors goes like the following:

(i) The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side.
(ii) All distances parallel to the principal axis are measured from the pole of the mirror.
(iii) The distances measured (from the pole) in the same direction as that of incident light are taken as positive.
(iv) The distances measured (from the pole) against the direction of incident light are taken as negative.
(v) Heights measured perpendicular to and above the principal axis (along + y-axis) are taken as positive.
(vi) Heights measured perpendicular to and below the principal axis (along – y-axis) are taken as negative.

The New Cartesian Sign Convention for spherical mirrors is shown in figure 1 below.

The New Cartesian Sign Convention for spherical mirrors
Figure 1: The New Cartesian Sign Convention for spherical mirrors

Distances – sign convention of spherical mirrors

  • All the distances measured from the pole (P) of the mirror to the right side will be considered positive (because they will be in the same direction as the incident light).
  • On the other hand, all the distances measured from the pole (P) of the mirror to the left side are considered negative (because they are measured against the direction of incident light).

focal length – sign convention of mirrors

On the basis of New Cartesian Sign Convention, the focal length of a convex mirror is considered positive (and written with a plus sign).

On the other hand, the focal length of a concave mirror is considered negative (and written with a minus sign).

The focal length of a convex mirror is positive and that of a concave mirror is negative.

Consequences of the new Cartesian sign convention for mirrors

1) The focal length of a convex mirror is positive and that of a concave mirror is negative.

2) Object distance u is always negative.

3) The distance of real image is negative and that of virtual image is positive. (for mirrors)

4) The object height h is always positive. Height h’ of virtual erect image is positive and that of real inverted image is negative.

5) The linear magnification, m = h’/h is positive for a virtual image and negative for a real image.

Also read this side by side Sign convention for spherical lenses

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