Question

Explain the sign convention for the spherical mirror.

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Solution

Sign in the case of the concave mirror: Since the object is always placed in front of the mirror hence the sign of object is taken as negative. Since the centre of curvature and focus lie in front of the concave mirror, so signs of the radius of curvature and focal length are taken as negative in the case of the concave mirror. When an image is formed in front of the mirror, the distance of image is taken as – (negative) and when the image is formed behind the mirror, the distance of image is taken as + (positive). The height of the image is taken as positive in the case of erect image and taken as negative in the case of an inverted image. Sign in the case of the convex mirror: Since object is always placed in front of the mirror hence the sign of object is taken as negative. Since, the centre of curvature and focus lies behind the convex mirror, so sign of radius of curvature and focal length are taken as + (positive) in the case of convex mirror. In the case of convex mirror, image always formed behind the mirror, thus the distance of image is taken as positive. In the case of a convex mirror, always an erect image is formed, thus the height of image is taken as positive.

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