A 3.0-cm-tall object is 22.4 cm from a concave mirror. If the mirror has a radius of curvature of 34.0 cm, what is the image height
To find the image height of the object, we can use the mirror equation:
1/f = 1/do + 1/di
where:
- f is the focal length of the mirror,
- do is the object distance (distance from the mirror to the object),
- di is the image distance (distance from the mirror to the image).
In this case, the mirror is concave, so the focal length (f) is half the radius of curvature (R):
f = R/2 = 34.0 cm / 2 = 17.0 cm.
The object distance (do) is given as 22.4 cm.
Now, we can rearrange the mirror equation to solve for the image distance (di):
1/di = 1/f - 1/do,
di = 1 / (1/f - 1/do).
Substituting the given values, we have:
di = 1 / (1/17.0 - 1/22.4).
Now we can calculate the value of di.
Finally, to find the image height (hi), we can use the magnification equation:
hi/ho = - di/do,
where:
- hi is the image height,
- ho is the object height.
The object height (ho) is given as 3.0 cm.
Now we can substitute the calculated values of di, do, and ho into the magnification equation to find hi.