A 8.20 cm tall object is placed 30.0 cm in front of a concave mirror with a focal length of 4.20 cm. What is the magnification?
To find the magnification of an object placed in front of a concave mirror, you can use the magnification formula:
Magnification (m) = height of image (hi) / height of object (ho)
In this case, the height of the object is given as 8.20 cm, and we need to find the height of the image.
To determine the height of the image, we can use the mirror equation:
1/f = 1/di + 1/do
Where:
- f is the focal length of the mirror,
- di is the distance of the image from the mirror, and
- do is the distance of the object from the mirror.
Given:
- f = 4.20 cm
- do = 30.0 cm
We can rearrange the mirror equation to solve for di:
1/di = 1/f - 1/do
Now, substitute the known values:
1/di = 1/4.20 cm - 1/30.0 cm
Simplify the equation:
1/di = 0.2381 cm^-1 - 0.0333 cm^-1
1/di = 0.2048 cm^-1
di = 1 / 0.2048 cm^-1
di ≈ 4.88 cm
Now that we have the distance of the image from the mirror (di), we can find the height of the image (hi). In this case, the height of the image will be negative because the mirror is concave.
Using the magnification formula:
m = hi / ho
We have:
- ho = 8.20 cm
- di ≈ 4.88 cm
Substituting the values:
m = hi / 8.20 cm = (−4.88 cm) / 8.20 cm
m ≈ -0.5951
Therefore, the magnification of the object is approximately -0.5951.