find the height of an image formed in a concave mirror with a 4.0cm focal length if the height of the objact is 2.5cm and it is 1.6 cm from the mirror.
To find the height of an image formed in a concave mirror, you can use the mirror equation:
1/f = 1/do + 1/di,
where:
- f is the focal length of the mirror,
- do is the distance between the object and the mirror, and
- di is the distance between the image and the mirror.
In this case, the focal length (f) is given as 4.0 cm. The distance between the object (do) and the mirror is 1.6 cm.
Rearranging the mirror equation to solve for di, we get:
1/di = 1/f - 1/do
Substituting the given values into the equation, we have:
1/di = 1/4 - 1/1.6
Now, we can calculate the value of 1/di:
1/di = 0.25 - 0.625 = -0.375
To find di, take the reciprocal of 1/di:
di = -1 / (-0.375) = 2.67 cm
Now, to calculate the height of the image (hi), we can use the magnification equation:
hi / ho = -di / do,
where:
- hi is the height of the image, and
- ho is the height of the object.
Substituting the given values into the equation, we have:
hi / 2.5 = 2.67 / 1.6
Now, solve for hi:
hi = (2.67 / 1.6) * 2.5 = 4.17 cm.
So, the height of the image formed in the concave mirror is approximately 4.17 cm.