Question

(i)A 1 cm object is placed perpendicular to principal axis of a convex mirror of focal length 7.5 cm.
Find its distance from mirror of the image formed is 0.6 cm in size
(ii)A man uses a concave mirror for shaving He keeps his face at a distance of 25 cm from the mirror and image is 1.4 times enlarged.Find the focal length of the mirror.
(iii)A particle goes in a circle of radius 2.0 cm.A concave mirror of focal length 20 cm is placed with its principle axis passing through the center of the circle and perpendicular to plane.The distance between the pole of the mirror and center of the circle is 30 cm. Calculate radius of circle formed by the image.
please answer all questions with detailed steps with proper explanation.

Answer 1

$m=-\frac{v}{u}=-\frac{h'}{h}=\frac{0.6}{1}=0.6,\ \ v=-0.6u \\\\ \frac{1}{v}+\frac{1}{u}=\frac{1}{f}\\\\-\frac{1}{0.6u}+\frac{1}{u}=\frac{1}{7.5}\\\\u=-1.25 cm.$
====================================

$m=1.4=-\frac{v}{u}\\\\ v=-1.4*(-25)=35cm \\\\\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\\\\\frac{1}{35}+\frac{1}{-25}=\frac{1}{f}\\\\ f= -87.5 cm$

======================

$u=-30\ cm,\ R=2\ cm.\\\\\frac{1}{v}=\frac{1}{f}-\frac{1}{u}\\\\\frac{1}{v}=\frac{1}{-20}-\frac{1}{-30}\\\\v=-60\ cm\\ \\m=-\frac{v}{u}=\frac{R'}{R}=-2.\\\\Image\ of\ particle\ will\ be\ in\ a\ circle\ of\ radius= R'=2*R=4\ cm$

The line joining the particle and the center of circle it is revolving in, acts as the object for the concave mirror.  The radius of the circle in which the image of particle moves acts as the image of the radius of the particle.