The image of an object is located 6cm behind a convex mirror. If its magnification is 0.6, calculate the focal length of the mirror

Answer Details

The magnification of a mirror is given by the ratio of the height of the image to the height of the object. magnification (m) = height of image (h') / height of object (h) Also, for a convex mirror, the focal length (f) is negative, and the relationship between the focal length, image distance (v) and object distance (u) is given by the mirror equation: 1/f = 1/v + 1/u where u is the distance of the object from the mirror, and v is the distance of the image from the mirror. Given that the magnification of the mirror is 0.6, we know that: m = h'/h = 0.6 We also know that v = -6 cm (since the image is behind the mirror), and we can assume that the object is far enough away from the mirror that u can be considered infinite. Using the magnification equation, we can write: 0.6 = h'/h = -v/u Solving for u, we get: u = -v/h' = -6 / 0.6 = -10 cm Substituting these values into the mirror equation, we get: 1/f = 1/v + 1/u = -1/6 - 1/(-10) = -5/30 + 3/30 = -2/30 Simplifying, we get: f = -15 cm Therefore, the focal length of the convex mirror is 15 cm, which corresponds to.