The linear magnification produced by a spherical mirror i.e $- \frac{1}{5}$ . Analysing this value state the (i) type of spherical mirror and (ii) the position of the object with respect to the pole of the mirror. Draw a ray diagram to justify your answer.

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Solution

The question says that the linear magnification of the spherical mirror is $m = - \frac{1}{5}$ , therefore the magnification is negative in the only case of a concave mirror and for real and inverted image. The equation for the linear magnification is given as,
$m = - \frac{1}{5} = \frac{h_{1}}{h_{0}} = \frac{v}{u}$
where,
$h_{1}$ =height of image
$h_{0}$ =height of object
u =object's distance
v=image distance
This equation shows that the height of the object is five times the height of its image, also the distance of the object from the pole of the mirror is five times the distance of its image from the pole. Thus, the ray diagram for the same will be given as,

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