The image of a crayon appears to be 20.6 cm
behind the surface of a convex mirror and is 1.64 cm tall. The mirror’s focal length is 54.3
cm.
a) How far in front of the mirror is the
crayon positioned?
Answer in units of cm
I keep on getting it wrong so the answer & explanation would be much appreciated.
disregard
To find the distance in front of the mirror where the crayon is positioned, we can use the mirror formula:
1/f = 1/di + 1/do
Where:
- f is the focal length of the mirror,
- di is the distance of the object (crayon) from the mirror (negative since it is behind the mirror), and
- do is the distance of the image from the mirror (positive since it is in front of the mirror).
Given:
- The focal length (f) is 54.3 cm.
- The image distance (do) is 20.6 cm (positive since it is in front of the mirror).
We need to find the object distance (di), which is the unknown in this case.
Rearranging the formula, we get:
1/do = 1/f - 1/di
Substituting the known values:
1/20.6 = 1/54.3 - 1/di
Now, we can solve for di:
1/di = 1/20.6 - 1/54.3
Taking the reciprocal of both sides:
di = 54.3 * 20.6 / (54.3 - 20.6)
di = 18.152 cm
Therefore, the crayon is positioned approximately 18.152 cm in front of the convex mirror.