A convex mirror has a focal length of 15 cm. A 3.0 cm high object is located 10 cm in front of this mirror. Where is the image located?
To determine the location of the image formed by a convex mirror, we can use the mirror equation:
1/f = 1/di + 1/do
Where f is the focal length of the mirror, di is the distance of the image from the mirror, and do is the distance of the object from the mirror.
Given:
focal length (f) = 15 cm
distance of the object (do) = -10 cm (since it is in front of the mirror)
We need to calculate the distance of the image (di).
Substituting the values into the mirror equation:
1/15 = 1/di + 1/-10
To solve for di, we need to isolate it on one side of the equation.
Multiplying both sides of the equation by -150di:
-10di = -150 + 15di
Moving the terms involving di to one side:
-25di = -150
Dividing both sides by -25:
di = 6
Therefore, the image is located approximately 6 cm behind the mirror.