An object that is 19 cm in front of a convex mirror has an image located 24 cm behind the mirror. How far behind the mirror is the image located when the object is 12 cm in front of the mirror?
I found that 1/Di = 1/-24 + 1/19 - 1/12 = -.07236.
And that means that f= -13.82. But I am being told that this is wrong. Can you please help??
The answer should be positive, so 13.82 is correct
To determine the distance of the image when the object is 12 cm in front of the convex mirror, we can use the mirror equation:
1/f = 1/do + 1/di
Where:
f = focal length of the convex mirror
do = distance of the object from the mirror
di = distance of the image from the mirror
We are given the distance of the object (do = 12 cm) and the distance of the image when the object is 19 cm in front of the mirror (di = -24 cm).
Substituting the values into the equation:
1/f = 1/12 + 1/-24
To find the focal length (f), we need to solve for it. Let's calculate the equation:
1/f = 1/12 - 1/24
1/f = (2 - 1) / 24
1/f = 1/24
f = 24 cm
Now that we know the focal length is 24 cm, we can find the distance of the image (di) when the object is 12 cm in front of the mirror:
1/f = 1/do + 1/di
1/24 = 1/12 + 1/di
To find di, we can solve the equation:
1/di = 1/24 - 1/12
1/di = 2 - 4 / 48
1/di = -2 / 48
1/di = -1/24
Therefore, di = -24 cm.
So, the image is located 24 cm behind the mirror when the object is 12 cm in front of the mirror.