Ed(height of 2.3 m) is 30 m away from the passenger side of a car. The radius of curvature of the mirror is -4m.
How far from the mirror is the image?
Is the image virtual or real?
How tall is the image?
To find the distance from the mirror at which the image is formed, we can use the mirror formula:
1/f = 1/di + 1/do
where:
f = focal length of the mirror (which is equal to half the radius of curvature)
di = distance of the image from the mirror
do = distance of the object from the mirror (given as 30m)
Given that the radius of curvature is -4m, the focal length (f) is -2m.
Substituting the values into the mirror formula:
1/-2 = 1/di + 1/30
To find di, we solve for it:
1/di = 1/-2 - 1/30
1/di = -15/30 - 1/30
1/di = -16/30
di = -30/16 = -1.875m
Since the distance (di) is negative, it means the image is formed on the same side as the object. Therefore, the distance from the mirror to the image is 1.875m away from the mirror.
To determine if the image is virtual or real, we look at the sign of the image distance (di). In this case, since di is negative, the image is virtual.
To find the height of the image, we can use the magnification formula:
magnification = -di/do
Substituting the given values:
magnification = -(-1.875) / 30
magnification = 1.875 / 30
magnification = 0.0625
The magnification tells us that the image is 0.0625 times the size of the object. Therefore, the height of the image is:
height of image = magnification * height of object
height of image = 0.0625 * 2.3m
height of image = 0.144m or 14.4 cm
Hence, the image is formed 1.875m away from the mirror, it is virtual, and its height is 0.144m (or 14.4 cm).