rex stands 3m away from a concave mirror.his hieght is 1.70m. If the image formed on the screen is 12cm from the mirror,what is the size of the image
Rex stands 3m away from a concave mirror. His height is 1.70 m. If the image formed is 12 cm from the mirror, what is the size of the image?
To determine the size of the image formed by the concave mirror, we can use the magnification formula:
magnification = - (image distance) / (object distance).
Given:
Object distance (o) = 3m.
Image distance (i) = 12cm = 0.12m. (Note: Convert cm to meters before plugging it into the formula).
Now, let's calculate the magnification:
magnification = - (0.12m) / (3m)
magnification = - 0.04
The negative sign indicates that the image is inverted.
To find the size of the image, we can use the formula:
size of the image = magnification x size of the object.
Given:
Size of the object (h) = 1.70m.
size of the image = (-0.04) x (1.70m)
size of the image = - 0.068m
Therefore, the size of the image formed by the concave mirror is approximately -0.068 meters.
To find the size of the image, we can use the magnification formula for concave mirrors:
magnification (m) = -image distance (di) / object distance (do)
Where:
- The magnification (m) represents the size of the image relative to the size of the object.
- The image distance (di) is the distance between the mirror and the image.
- The object distance (do) is the distance between the mirror and the object.
Given:
- Object distance (do) = 3m (Rex is 3m away from the mirror)
- Image distance (di) = 12cm = 0.12m (The image is formed 12cm away from the mirror)
- The height of Rex (ho) = 1.70m
Now, let's calculate the magnification:
m = -di / do
m = -0.12 / 3
m = -0.04
Since the magnification is negative, it implies that the image is inverted.
To find the size of the image, we can multiply the magnification (m) by the object height (ho):
Image height (hi) = m * ho
hi = -0.04 * 1.70
hi = -0.068m
The "-" sign indicates that the image is inverted.
Therefore, the size of the image is approximately 0.068 meters.