Chapter 29, Problem 54A

What effect does your distance from the mirror have on the answer to Activity 53? (Hint: Move closer and farther from your initial position. Be sure the top of your head lines up with the top piece of tape. At greater distances, is your image smaller than, larger than, or the same size as the space between the pieces of tape?) Are you surprised?

To determine

When the distance between the person and plane mirror changing, what would happen to the image size.

Explanation of Solution

Introduction:

When an object is placed in front of a plane mirror, it will produce similar image.

The mirrors will always produce virtual images. The image distance is always equal to object distance. As the object and image distance are equal, the magnification of the plane mirror becomes one.

  $m=-\frac{v}{u}$

Here, m is the magnification, v is the image distance and u is the object distance.

For a plane mirror, $v=u$

Then, the magnification becomes

  $\begin{array}{l}m=-\frac{v}{u}\\ m=-\frac{(-u)}{u}\\ m=1\end{array}$

(negative sign is due to virtual nature of image)

Therefore, even if the person moves away from the mirror, along with the object distance, image distance will also change so the magnification remains 1.

Conclusion:

Therefore, the image size will not change upon increasing the distance between the person and the plane mirror.