# How to Measure a Magnification Mirror

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A magnifying mirror, otherwise known as a concave mirror, is a reflecting surface that constitutes a segment of the inner surface of a sphere. For this reason, concave mirrors are classed as spherical mirrors. When objects are positioned between the focal point of a concave mirror and the mirror's surface, or the vertex, the images seen are “virtual”, upright and magnified. When objects are beyond the focal point of the mirror, the images seen are real images, but they are inverted. The magnification of a spherical mirror image can be determined, analytically, if either the focal length or center of curvature of the mirror is known.

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.

#### Tips

• The focal length of a mirror is the distance to the focal point, which is the point midway between the geometric center or vertex of the mirror and the center of curvature of the mirror.

The center of curvature of a mirror is the point in the center of the sphere from which the mirror is cut.

A virtual mirror image is an image from which rays of reflected light appear to diverge.