Question

A convex mirror with an aperture diameter of 60cm has a magnitude of focal length 4m. A person is standing 4.0 m from the mirror and looking at a wide wall behind him. The distance of the wall from the mirror is 58m. What is the width of the section of the wall seen in the mirror

Answer 1

Approximately 9.3 m

Answer 2

1. For a convex mirror the mirror‐formula is

   $\frac{1}{v}=\frac{1}{f} - \frac{1}{u}$,

   with $f = -4\,\text{m}$ (negative for convex) and for the wall $u = 58\,\text{m}$.

2. Calculate the image distance $v$ of the wall:

   $$\frac{1}{v} = \frac{1}{-4} - \frac{1}{58} = -0.25 - 0.01724 \approx -0.26724,$$ $$v \approx -3.744\,\text{m}.$$

   (The negative $v$ tells us the image is virtual, behind the mirror.)

3. The magnification (in absolute value) is:

   $$|m|=\left|\frac{v}{u}\right| = \frac{3.744}{58} \approx 0.06455.$$

4. The convex mirror has an aperture of $0.60\,\text{m}$ (i.e. a diameter of 0.6 m). This means that only an image of thickness 0.60 m is produced. The corresponding actual (object) size on the wall is

   $$\Delta y_{\text{wall}} = \frac{0.60}{|m|} \approx \frac{0.60}{0.06455} \approx 9.285\,\text{m}.$$

5. Thus, approximately 9.3 m of the wall’s width is seen in the mirror.