B PA . The triangles ∆ BPA and ∆ ′ ′ B PA are similar. Thus, from the rule of similar triangles, ′ ′ = ′ A B AB PA PA ( . ) The other set of similar triangles are, ∆ DPF and ∆ ′ ′ B A F .
( PD is almost a straight vertical line) (iv) A ray falling on the pole will get reflected as per law of reflection keeping principal axis as the normal. (Figure . (d)) . .
Cartesian sign convention While tracing the image, we would normally come across the object distance u , the image distance v , the object height h , the image height ′ h , the focal length f and the radius of curvature R . A system of signs for these quantities must be followed so that the relations connecting them are consistent in all types of physical situations. We shall follow the Cartesian sign convention which is now widely used. It is given below and also shown in Figure .
. (i) The Incident light is taken as if it is travelling from left to right (i.e. object on the left of mirror). (ii) All the distances are measured from the pole of the mirror (pole is taken as origin).
(iii) The distances measured to the right of pole along the principal axis are taken as positive. (iv) The distances measured to the left of pole along the principal axis are taken as negative. (v) Heights measured upwards perpendicular to the principal axis are taken as positive. (vi) Heights measured downwards perpendicular to the principal axis, are taken as negative.
Pole (P) Height upwards (Positive) Height downwards (Negative) Incident light Distance to the lef (Negative) Distance to the right (Positive) Figure . Cartesian sign convention - - - - Unit ray optics The equation ( . ) is called mirror equation . Although this equation is derived for a special situation shown in Figure ( .
), it is also valid for all other situations with any spherical mirror. This is because proper sign convention is followed