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Sign Convention For Spherical Mirrors

Physics Topics cover a broad range of concepts that are essential to understanding the natural world.

Give the Sign Convention in Concave and Convex mirrors.

These days New Cartesian Sign Convention is used for measuring the various distances in the ray- diagrams of spherical mirrors (concave mirrors and convex mirrors). According to the New Cartesian Sign Convention :

  1. All the distances are measured from pole of the mirror as origin.
  2. Distances measured in the same direction as that of incident light are taken as positive.
  3. Distances measured against the direction of incident light are taken as negative.
  4. Distances measured upward and perpendicular to the principal axis are taken as positive.
  5. Distances measured downward and perpendicular to the principal axis are taken as negative.

The New Cartesian Sign Convention for mirrors is shown in Figure.
Sign Convention For Spherical Mirrors 1
The object is always placed on the left side of the mirror (as shown in Figure) so that the direction of incident light is from left to right. Since the incident light always goes from left to right, all the distances measured from the pole (P) of 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 pole (P) of mirror to the left side will be negative (because they are measured against the direction of incident light).

Some Important Conclusions

According to the sign convention, the distances towards the left of the mirror are negative. Since an object is always placed to the left side of a mirror, therefore, the object distance (u) is always negative.

The images formed by a concave mirror can be either behind the mirror (virtual) or in front of the mirror (real). So, the image distance (υ) for a concave mirror can be either positive or negative depending on the position of the image. If an image is formed behind a concave mirror (to the right side), the image distance (υ) is positive but if the image is formed in front of the mirror (on the left side), then the image distance will be negative.

In a convex mirror, the image is always formed on the right hand side (behind the mirror), so the image distance (υ) for a convex mirror will be always positive.

The focus of concave mirror is in front of the mirror on the left side, so the focal length of a concave mirror is considered negative (and written with a minus sign, say, -10 cm). On the other hand, the focus of a convex mirror is behind the mirror on the right side, so the focal length of a convex mirror is positive (and written with a plus sign, say +20 cm or just 20 cm).

We will now discuss the signs for the heights of objects and images. An object is always placed above the principal axis in the upward direction, so the height of an object is always considered positive. On the other hand, an image can be formed above the principal axis or below the principal axis.

If an image is formed above the principal axis, its height is taken as positive and if an image is formed below the principal axis, then its height is taken as negative. Now, we know that all the virtual images are erect and are formed above the principal axis, so the height of all the virtual and erect images is considered positive.

On the other hand, all the real images are inverted and they are formed below the principal axis, so the height of all the real and inverted images is taken as negative.

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