Question

a mobile phone lies along the principal axis of a concave mirror .In image formation why the magnification is not uniform .Will the distortion of image depend on the location of the phone with respect to the mirror.

Answer 1

QUESTION:

a mobile phone lies along the principal axis of a concave mirror. In image formation why the magnification is not uniform. Will the distortion of image depend on the location of the phone with respect to the mirror.

SOLUTION:

The magnification $m$ of a curved mirror is defined as the height of the image $h_{im}$ divided by the height of the object $h_{ob}$:

$$m = \frac{h_{im}}{h_{ob}}$$

And from the mirror equation

$$\frac{1}{d_{ob}} + \frac{1}{d_{im}} = \frac{1}{f} = \frac{2}{R}$$

we can derive

$$m = \frac{h_{im}}{h_{ob}} = \left| \frac{d_{im}}{d_{ob}} \right|$$

Where $d_{im}$ – the image distance, and $d_{ob}$ – object distance. As $d_{im}$ is nonlinear function of $d_{ob}$ the magnification is not uniform and the image distortion depends on the location of the object with the respect to the mirror