Answer:
f ≈ 6.369 m
Step-by-step explanation:
For a convex mirror, the magnification is negative, and it is given by:
m = -v/u
where
m = magnification
v = image distance
u = object distance
We are given:
m = -0.57
u = -3.6 m (negative sign indicates the object is in front of the mirror, i.e., on the same side as the incident light)
To find the focal length, we can use the mirror formula:
1/f = 1/v + 1/u
where f is the focal length.
Substituting the given values, we get:
1/f = 1/v + 1/u
1/f = 1/(-v) - 1/3.6
1/f = (-1/v) - (1/3.6)
1/f = (-0.57/(-3.6)) - (1/3.6)
1/f = 0.157
f = 1/0.157
f ≈ 6.369 m
Therefore, the focal length of the convex mirror is approximately 6.369 meters.