An object is placed at a certain distance from a convex mirror of focal length 20 cm. Find the distance of the object if the image obtained is magnified 4 times.
To find the distance of the object from the convex mirror, we can use the mirror equation:
1/f = 1/do + 1/di
Where:
- f is the focal length of the convex mirror
- do is the distance of the object from the mirror
- di is the distance of the image from the mirror
Since we know that the image is magnified 4 times, we also know that the magnification (M) is equal to -di/do. In this case, M = -4.
Using the magnification formula, we have:
M = -di/do
-4 = -di/do
Now we can rearrange the mirror equation to solve for do:
1/f = 1/do + 1/di
1/20cm = 1/do + -1/(-4do) (replacing di with -4do due to the magnification)
1/20cm = 1/do + 1/4do
1/20cm = (1 + 1/4)/do
1/20cm = 5/4do
Now we can cross-multiply to solve for do:
1 × 4do = 20cm × 5
4do = 100cm
do = 100cm / 4
do = 25cm
Therefore, the distance of the object from the convex mirror is 25 cm.