A convex mirror with focal length of -20 cm forms an image 12 cm behind the surface. Where is the object located as measured from the surface?
To find the location of the object, we can use the mirror formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the mirror
- v is the image distance
- u is the object distance
In this case, we have the focal length (f) as -20 cm and the image distance (v) as 12 cm. We need to find the object distance (u).
Rearranging the formula to solve for u, we have:
1/u = 1/f - 1/v
Substituting the given values:
1/u = 1/(-20 cm) - 1/12 cm
To simplify the equation, let's find the common denominator:
1/u = (-12 + 20) / (-20 * 12) cm
1/u = 8 / (-20 * 12) cm
1/u = -1 / (20 * 3) cm
Now, let's invert both sides of the equation to solve for u:
u = - (20 * 3) / 1 cm
u = -60 cm
Therefore, the object is located 60 cm in front of the mirror surface.