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.