Determine the location of an image formed by a convex mirror by using the "mirror equation," which relates object distance (D object), image distance (D image), and focal length (F) of the mirror as follows:
1/(D object) + 1/(D image) = 1/F.
The focal length is the distance between the mirror and the point where rays of light emanating from an object converge. You will need to know the value of F in order to locate images formed by a mirror.
Determine the height of an image by using the "mirror magnification relation," which relates image height (H image), object height (H object), image distance (D image) and object distance (D object) as follows:
M = (H image)/(H object) = (D image)/(D object)
Note that the distance ratio is the same as the height ratio.
Consider the following example: A lamp 10 inches tall is placed 80 inches from a convex mirror that has a focal length of -15 inches. Note that the focal length is negative because the focal point of a convex mirror is behind the mirror, not in front of the mirror.
Determine the distance of the lamp's image as follows:
1/f = 1/(D object) + 1/(D image)
1/-15 = 1/80 + 1/(D image)
1/(D image) = -1/15 - 1/80 = -0.0667 - 0.0125 = -0.0792
(D image) = 1/-0.0792 = -12.63.
So the image is located behind the mirror (indicated by the negative sign) at a distance of 12.63 inches.
Determine the height of the lamp's image by using the mirror magnification relation, as follows: (D image)/(D object) = 12.63/80; therefore (H image)/(H object) = 12.63/80 = 0.1578, and (H image) = 0.1578 x 10 = 1.58 inches.