Chapter 23, Problem 2Q

What is the focal length of a plane mirror? What is the magnification of a plane mirror?

To determine

The focal length of a plane mirror and the magnification of a plane mirror

Answer to Problem 2Q

Solution:

The focal length of a plane mirror is infinity. The magnification of a plane mirror is one.

Explanation of Solution

Given:

A plane mirror

Formula used:

The mirror equation is given by

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

Where

$f\text{ is the focal length}$

${\text{d}}_o\text{ is the distance of the object from the mirror}$

${\text{d}}_i\text{ is the distance of the image from the mirror}$

The magnification, m, of a mirror is given by

$m=-\frac{d_i}{d_o}$

Where, the negative sign indicates as the convention.

Calculation:

The image of a plane mirror will always be upright, same size as the object and will be located far behind the mirror as the object is in front of the mirror.

The image formed by the plane mirror is the virtual image formed behind the mirror. The distance from the image to the mirror is always identical to the distance from the object to the mirror.

A spherical mirror becomes equivalent to a plane mirror when the limit of is radius of curvature tends to infinity.

Hence, the mirror formula can be applied to the plane mirror also.

The plane mirror, the distance of the object is equal to the distance of the image and the image is formed behind the mirror. Hence,

$d_o=-d_i$

Then, the focal length is given by

$\frac{1}{f}=\frac{1}{d_o}-\frac{1}{d_o}=0$

$f=\infty$

Then, the magnification of the plane mirror is

$m=-\frac{d_0}{-d_o}$

$m=1$