List the new Cartesian sign convention for reflection of light by spherical mirrors. Apply these conventions for calculating the focal length and nature of a spherical mirror which forms a 1/3 times magnified virtual image of an object placed 18 cm in front of it.
The Sign conventions for reflection of light by spherical mirrors are as follows:
(i) The pole is taken as the origin and all the distances are measured from pole of the mirror.
(ii) In case of spherical mirror, the objects are always placed in left of the mirror.
(iii) All the distances which are measured in the direction of light incidence, is taken as positive and all the distances which are measured against the direction of incident light are taken as negative.
(iv) The perpendicular distances to principal axis in upward direction will be positive and those in downward direction will be taken as negative.
The sign conventions can be expressed in tabular form as follows for various mirrors and different positions of the object:
Types of mirror | Position of object | Magnification | Image distance | Focal length | Height of object | Height of the image |
Concave | Between P&F | Negative | Positive | Negative | Positive | Positive |
Concave | Between F & C | Negative | Negative | Negative | Positive | Negative |
Concave | At C | Negative | Negative | Negative | Positive | Negative |
Concave | Beyond C | Negative | Negative | Negative | Positive | Negative |
Convex | In front of it | Negative | Positive | Positive | Positive | Positive |
Given: Object distance, u = -18 cm
Magnification, m = 1/3
Magnification is given by the relation
On calculating we get v=+6 cm
Now, applying the lens formula which is given as:
Therefore, focal length f=9 cm
Since focal length is positive, therefore the lens is a convex lens.
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