Study the following equation, called the "mirror equation," which relates the distance of an object (D object), the distance of the image (D image) and the focal length (F) of the mirror: 1/D object + 1/D image = I/F. The image distance must first be determined with this equation before the image magnification can be determined.
Consider the following example: an object 12 inches tall is placed a distance of 4 inches from a concave mirror that has a focal length of 6 inches. How do you find the image distance and magnification?
Substitute the required information into the mirror equation, as follows: 1/4 + 1/D image = 1/6; 1/D image = 1/6 -- 1/4 = - (1/12); D image = - 12. The image is a virtual image, not a real image: it "appears" to be located 12 inches behind the mirror, hence the negative sign.
Study the following equation, called the "mirror magnification equation," which relates the height of the image (H image), the height of the object (H object), D image and D object: M = H image/H object = - (D image/D object). Note the distance ratio is the same as the height ratio. The negative sign remains in the result only if the image turns out to be inverted, instead of upright.
Substitute the required information into the mirror magnification equation, as follows: M = - (D image/D object) = - (- 12/4) = 3. The image is upright and three times larger than the object.