when an object is placed 8 millimeters from a concave spherical mirror, a clear image can be projected on a screen 16 millimeters in front of a mirror,If the object has a height of 4 millimeters, the height of the image is
8 mm.
The ratio Di/Do is the magnification, which in this case is 2.
To determine the height of the image formed by a concave spherical mirror, we can make use of the mirror formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the mirror
- v is the image distance (distance between the mirror and the image)
- u is the object distance (distance between the mirror and the object)
Given:
- Object distance (u) = 8 mm
- Image distance (v) = 16 mm
We need to find the height of the image formed, denoted by 'h'. The magnification formula can help us find this value:
magnification (m) = -v/u = h'/h
Where:
- h' is the height of the image formed
- h is the height of the object
Rearranging the formula, we have:
h' = m * h
Let's calculate the magnification (m) using the formula:
m = -v/u = -16/8 = -2
Now, substitute the known values into the equation to find the height of the image:
h' = -2 * 4
h' = -8
The height of the image formed by the concave spherical mirror is -8 mm. The negative sign indicates that the image is inverted.