Giving reasons, state the 'signs' (positive or negative) which can be given to the following:(a) object distance (u) for a concave mirror or convex mirror(b) image distance (v) for a concave mirror(c) image distance (v) for a convex mirror

(a) Object distance $(u)$ for a concave mirror or convex mirror is always negative $(-)$, because the object is always placed to the left of the mirror, and the distances towards the left of the mirror are always negative $(-)$ (​according to the 'new cartesian sign convention').

(b) In the case of a concave mirror, if the image is formed on the left side or in front of the mirror, then the image distance $(v)$ will be negative $(-)$, and if the image is formed on the right side or behind the mirror, then the image distance $(v)$ will be positive $(+)$. This is because according to the 'new cartesian sign convention' distances measured to the left of the mirror are negative and to the right of the mirror is positive.

(c) The image distance $(v)$ for a convex mirror is always given a positive sign $(+)$ because the image is always formed behind the mirror and to the right of it. And, according to the 'new cartesian sign convention' distances measured to the left of the mirror are negative and to the right of the mirror is positive.

Explanation

According to the New Cartesian Sign Convention, all the distances are measured from the pole of a spherical mirror.

The distances on the left side of the mirror from the pole (in front of the mirror) are given a negative sign. On the other hand, distances on the right side of the mirror from the pole (behind the mirror) are given a positive sign. Also, the image formed below the axis or downwards,  it's given a negative sign, whereas the image formed above the axis or upwards, it's given a positive sign.

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Updated on: 10-Oct-2022

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