How far should and object be from a concave sperical mirror of radius 36cm to form a real image one-ninth it's size?
To determine the distance at which an object should be placed in front of a concave spherical mirror to form a real image, we can use the mirror formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the mirror
- v is the image distance from the mirror
- u is the object distance from the mirror
Given:
- The radius of the mirror, which is equal to half the focal length (r = f/2 = 36 cm)
- The magnification of the image (m = -1/9, since the image is one-ninth the size of the object)
Now, let's find the focal length of the mirror:
f = 2 * r
f = 2 * 36 cm
f = 72 cm
We can also calculate the image distance using the magnification formula:
m = v/u
-1/9 = v/u
Now, substituting the known values into the mirror formula:
1/72 = 1/v - 1/u
1/v = 1/72 + 1/u
Since we know that -1/9 = v/u, we can substitute this into the equation:
1/v = 1/72 + 9/u
Next, we subtract these fractions by finding a common denominator:
1/v = (1 + 72/9) / 72
1/v = (1 + 8) / 72
1/v = 9/72
1/v = 1/8
Thus, v = 8 cm.
Finally, we substitute v into the magnification formula to find u:
-1/9 = 8/u
u = -72 cm
Therefore, the object should be placed 72 cm in front of the concave spherical mirror to form a real image one-ninth its size.
180
Let the object distance be Do. The image distance must be Di = Do/9 to achieve the desired magnification.
The focal length of the mirror is
f = R/2 = 18 cm
Solve the basic equation
1/Do + 1/Di = 1/f
It isn't hard.