The image of a crayon appears to be 21.9 cm behind the surface of a convex mirror and is 2.93 cm tall. the mirror’s focal length is 49.1 cm.
a) how far in front of the mirror is the crayon positioned?
answer in units of cm.
b) calculate the magnification of the image.
c) describe the image.
1. virtual, upright, larger 2. virtual, inverted, larger 3. real, upright, larger
4. virtual, upright, smaller 5. real, inverted, larger
6. real, inverted, smaller
7. none of these
8. virtual, inverted, smaller 9. real, upright, smaller

d) how tall is the actual crayon? answer in units of cm.

In the 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

The Mirror Formula 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 negative signs indicate the focal distance and the distance between the image and the mirror are virtual

Then:

(3) >>>>Position of the crayon

The magnification of the image is given by:

  (4)

 (5)>>>the image is 0.553 smaller than the object

According to the explanations and results obtained in the prior answers, the correct option is 4:

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 the crayon

i think the answer would be b