Write any four main points of the new cartesian sign convention for reflection by spherical mirrors. if according of this convention, the radius of curvature of a spherical mirror is 30 cm, write the name and focal length of the mirror.
Answers
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.Focal length is half the radius of the mirror.
So f=30/2=15cm
With a spherical mirror this is not the focal length, as rays do not converge in one point, depending on their distance from the optical axis. But for small mirrors this will do.
The pole P of the spherical mirror is taken as the origin and the principal axis of the mirror is along the X-axis of the coordinate system.
Keeping this in mind, we can easily note the following facts:
(i) Object distance, u is always taken negative, because the object is placed on the left of the mirror.
(ii) In case of a concave mirror, a real image is formed in front (left side) of the mirror and a virtual image is formed behind (right side) the mirror, so image distance v is negative for a real image and positive for a virtual image.
(iii) In case of a convex mirror, the image distance v is always positive because the image is formed behind the mirror and is virtua.
(iv) The object height h is always taken positive, because the object is placed above the principal axis.
(v) The image height h' is taken negative for real image (as it lies below the principal axis) and the image height h' is taken positive for a virtual image (as it lies above the principal axis).
(vi) The focal length and radius of curvature of a concave mirror are taken negative because the principal focus lies on the left of the mirror.
(vii) The focal length and radius of curvature of a convex mirror are taken positive, because the principal focus lies on the right hand side of the mirror.
Now,
The radius of curvature = 30 cm
So,
Focal length = radius of curvature/2
= 30/2
= 15 cm
The mirror is having positive focal length, so, the mirror is Convex mirror.
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