an object 2.6 cm high is 24cm from concave mirror whose radius of curvature is 16cm. Determine the location of its image.
the answer is 12cm in front of mirror.
I want to know what to get this. What steps and which formulas are used?
please help
f=r/2
so f=16/2=8
1/di + 1/do = 1/f
1/di + 1/24 = 1/8
1/di= 1/8 - 1/24
1/di= 1/12
di = 12
magnification = - di/do
M = - 12/24 = -.5
To determine the location of the image formed by a concave mirror, you can use the mirror formula, which is:
1/f = 1/v - 1/u
Where:
- f is the focal length of the mirror
- u is the object distance from the mirror (positive for objects in front of the mirror)
- v is the image distance from the mirror (positive for real images in front of the mirror)
In this case, you are given:
- The object height (h) = 2.6 cm
- The distance of the object from the mirror (u) = 24 cm
- The radius of curvature (R) = 16 cm
First, we need to determine the focal length of the mirror using the formula: f = R/2. In this case, f = 16 cm / 2 = 8 cm.
Next, we can substitute the known values into the mirror formula:
1/f = 1/v - 1/u
Substituting the given values:
1/8 = 1/v - 1/24
To find v, we can solve this equation algebraically:
1/v = 1/8 + 1/24
1/v = (3 + 1) / 24
1/v = 4/24
1/v = 1/6
v = 6 cm
Since v is positive, it means that the image is formed on the same side of the mirror as the object, and it is a real image. The image distance is 6 cm, which indicates that the image is formed 6 cm in front of the mirror. Therefore, the location of the image is 12 cm in front of the mirror (since the object distance is 24 cm and the image is half that distance).