with what sign conventions are used for reflection from a spherical mirror
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The following sign convention is used for measuring various distances in the ray diagrams of spherical mirrors: Object is always placed to the left of mirror. All distances are measured from the pole of the mirror.
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Sign Convention for Spherical Mirror:
Cartesian Sign Convention: In the case of spherical mirror all signs are taken from Pole of the spherical mirror, which is often called origin or origin point. This sign convention is known as New Cartesian Sign Convention.
Sign is taken as – (negative) from pole of a spherical mirror towards object along the principal axis. This means sign is always taken as – (negative) in front of a spherical mirror. For example; the distance of object is always taken as – (negative) in case of both types of spherical mirror, i.e. concave and convex mirrors.
Sign is taken as + (positive) behind the spherical mirror. For example if an image is formed behind the mirror, the distance of image is taken as + (positive) from pole along the principal axis.The height of is taken as + (positive) above the principal axis and taken as – (negative) below the principal axis.
Sign in the case of concave 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 lie in front of the concave mirror, so signs of radius of curvature and focal length are taken as negative in the case of concave mirror.When image is formed in front of the mirror, the distance of image is taken as – (negative) and when image is formed behind the mirror, the distance of image is taken as + (positive).Height of image is taken as positive in the case of erect image and taken as negative in the case of inverted image.
Sign in the case of a 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.
Sign Convention for Spherical Mirror:
Cartesian Sign Convention: In the case of spherical mirror all signs are taken from Pole of the spherical mirror, which is often called origin or origin point. This sign convention is known as New Cartesian Sign Convention.
Sign is taken as – (negative) from pole of a spherical mirror towards object along the principal axis. This means sign is always taken as – (negative) in front of a spherical mirror. For example; the distance of object is always taken as – (negative) in case of both types of spherical mirror, i.e. concave and convex mirrors.
Sign is taken as + (positive) behind the spherical mirror. For example if an image is formed behind the mirror, the distance of image is taken as + (positive) from pole along the principal axis.The height of is taken as + (positive) above the principal axis and taken as – (negative) below the principal axis.
Sign in the case of concave 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 lie in front of the concave mirror, so signs of radius of curvature and focal length are taken as negative in the case of concave mirror.When image is formed in front of the mirror, the distance of image is taken as – (negative) and when image is formed behind the mirror, the distance of image is taken as + (positive).Height of image is taken as positive in the case of erect image and taken as negative in the case of inverted image.
Sign in the case of a 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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