An object which is 0.52m tall is located 1.13m in front of a plane mirror.
How tall is the image as seen in the mirror?
To determine the height of the image as seen in the mirror, we can make use of the mirror equation, which states:
1/f = 1/di + 1/do
Where:
f - focal length of the mirror
di - distance of the image from the mirror
do - distance of the object from the mirror
For a plane mirror, the focal length is infinity, meaning the mirror does not have a specific focal point. As a result, 1/f is equal to zero.
Therefore, the equation simplifies to:
1/di = 1/do
Now, we can plug in the given values:
do = 1.13m
Using the equation above, we can calculate:
1/di = 1/1.13
Solving this equation, we find:
di ≈ 0.884m
This value represents the distance of the image from the mirror. To find the height of the image, we can use the magnification formula:
magnification (m) = -di/do
Since the magnification of a plane mirror is always equal to -1, the height of the image will be equal in magnitude but opposite in direction to the height of the object.
Given that the object's height is 0.52m, the height of the image as seen in the mirror will also be 0.52m, but it will be inverted relative to the object.