what is the magnification of an object 2cm tall when placed 10cm in front of a plane mirror?
To determine the magnification of an object when placed in front of a plane mirror, we can use the formula:
Magnification (m) = Image height (h') / Object height (h)
In this case, the object height (h) is given as 2cm, and it is placed 10cm in front of a plane mirror.
However, when an object is placed in front of a plane mirror, the image formed is virtual and appears to be the same distance behind the mirror as the object is in front of it. So, the object distance (u) and the image distance (v) are both equal to 10cm.
Using the mirror formula:
1/f = 1/v + 1/u
Since it is a plane mirror, the focal length (f) is considered infinite.
Thus, substituting the values:
1/∞ = 1/10 + 1/10
Simplifying the equation, we get:
0 = 1/10 + 1/10
0 = 2/10
Since the equation does not hold true, it means that the mirror formula does not apply to plane mirrors.
However, we know that the magnification for a plane mirror is always +1, which means the image formed is of the same size as the object and there is no change in size. So, in this case:
Magnification (m) = Image height (h') / Object height (h) = 1
Therefore, the magnification of an object 2cm tall when placed 10cm in front of a plane mirror is +1 (same size).
To find the magnification of an object when placed in front of a plane mirror, we need to use the mirror formula:
magnification (m) = -distance of image (di) / distance of object (do)
Here's how to calculate the magnification for the given scenario:
1. Find the distance of the image (di):
In the case of a plane mirror, the image formed is virtual, erect, and located behind the mirror at the same distance as the object. So, di will be equal to -do. In this case, since the object is 10cm in front of the mirror, the distance of the image would be -10cm.
2. Find the distance of the object (do):
The given question states that the object is placed 10cm in front of the mirror. Hence, do would be equal to 10cm.
3. Substitute the values into the magnification formula:
m = -di / do
m = -(-10cm) / 10cm
m = 10cm / 10cm
m = 1
Therefore, the magnification of the object when placed 10cm in front of a plane mirror is 1.