In convex mirrors the focus is virtual and the focal distance is negative. This is how the reflected rays diverge and only their extensions are cut at a point on the main axis, resulting in a virtual image of the real object .
<h2 /><h2>a) Position of the soda bottle (the object) </h2><h2 />The Mirror equation is:
(1)
Where:
is the focal distance
is the distance between the object and the mirror
is the distance between the image and the mirror
We already know the values of and
, let's find
from (1):
(2)
Taking into account the explanation at the beginign of this asnswer:
and
The <u>negative signs</u> indicate the <u>focal distance</u> and the <u>distance between the image and the mirror are virtual </u>
Then:
(3) >>>>Position of the soda bottle
The magnification of the image is given by:
(4)
(5)>>>the image is 0.47 smaller than the object
<h2>The fact that this value is positive means the image is upright </h2><h2>c) Describe the image </h2><h2 />
According to the explanations and results obtained in the prior answers, the correct option is 9:
<h2>The image is <u>virtual, upright, smaller</u> than the object </h2><h2 /><h2>d) Height of the soda bottle (object) </h2>Another way to find the magnification is by the following formula:
(6)
Where:
is the image height
is the object height
We already know the values of and
, let's find
:
(7)
(8) >>>height of thesoda bottle