An object is placed 10cm in front of a concave mirror whose curventure is 12cm. Calculate the position of the image and magnification
Solve and show full working
don't you have some formula like
1/d1 + 1/d2 = 1/f
or something like that?
To calculate the position of the image and magnification formed by a concave mirror, you can use the mirror formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the mirror
- v is the distance of the image from the mirror (positive for a real image, negative for a virtual image)
- u is the distance of the object from the mirror (positive)
First, let's calculate the focal length (f) of the mirror:
f = R/2
Where R is the radius of curvature. In this case, the curvature is given as 12 cm, so:
f = 12 cm / 2 = 6 cm
Now, let's substitute the known values into the mirror formula:
1/6 = 1/v - 1/10
Multiply through by 60 to remove fractions:
10 = 60/v - 6
Rearrange the equation to solve for v:
60/v = 10 + 6
60/v = 16
v = 60/16
v = 3.75 cm
So, the position of the image (v) is 3.75 cm in front of the mirror. Since v is positive, it indicates a real image formed on the same side as the object.
To calculate the magnification, you can use the magnification formula:
magnification = -v/u
Substitute the known values:
magnification = -3.75/10
magnification = -0.375
Therefore, the magnification of the image is -0.375, indicating that it is reduced in size and inverted.