Question

A spherical mirror is polished on both sides. When the concave side is used as a mirror, the magnification is 4.4. What is the magnification when the convex side is used as a mirror, the object remaining the same distance from the mirror?

Answer 1

Answer:

$m = \frac{-4.4}{7.4}$

Explanation:

magnification is the ratio of distance of image to distance of object

i.e. $m = -\frac{d_i}{d_o}$

$d_i = -4.4 d_o$

As per the lens equation,

$\frac{1}{d_o} + \frac{1}{d_i} = \frac{1}{f}$

We will calculate the focal length of the mirror

$\frac{1}{yd_o} + \frac{1}{-4.4d_o} = \frac{1}{f} \\\frac{4.4 -1}{4.4} \frac{1}{d_o} = \frac{1}{f}\\f = \frac{4.4}{3.4} d_o$

Now for convex mirror only the sign will change

Thus, focal length would be equal to

$f = - \frac{4.4}{3.4} d_o$

Plugging this value into lens equation, we get

$\frac{1}{d_o} + \frac{1}{d_i} = \frac{1}{f} \\\frac{1}{d_o} + \frac{1}{d_i} = \frac{-3.4}{4.4} \frac{1}{d_o} \\\frac{7.4}{4.4} \frac{1}{d_o} = \frac{1}{d_i}\\\frac{d_i}{d_o} = \frac{4.4}{7.4} \\m =- \frac{d_i}{d_o} \\\\m = - \frac{4.4}{7.4}$