What is the position of an image in a curved mirror if the object is 25cm from the concave mirror with a focal length of 5 cm? Show your work.
4.17 cm in front of the mirror
6.25 cm in front of the mirror
4.17 cm behind the mirror
6.25 cm behind the mirror
The position of the image can be found using the mirror equation:
1/f = 1/do + 1/di
where f is the focal length of the mirror, do is the object distance (distance of the object from the mirror), and di is the image distance (distance of the image from the mirror).
In this case, f = 5 cm and do = 25 cm. Solving for di:
1/5 = 1/25 + 1/di
(di - 25)/5di = 1/25
25(di - 25) = 5di
25di - 625 = 5di
20di = 625
di = 31.25 cm
Since the image distance is positive, the image is located on the same side of the mirror as the object, or in front of the mirror. The distance of the image from the mirror is:
di - do = 31.25 - 25 = 6.25 cm
Therefore, the position of the image is 6.25 cm in front of the mirror. Answer: 6.25 cm in front of the mirror.