An object 4 cm high is placed 15 cm from a concave mirror of focal length 5 cm. The size of the image is

Answer Details

This is a problem from optics involving the use of a concave mirror. When an object is placed in front of a concave mirror, the image formed can be real or virtual, depending on the position of the object relative to the mirror. In this problem, we are given the height and distance of the object from the mirror, as well as the focal length of the mirror.
To find the size of the image, we need to first determine the distance of the image from the mirror. We can use the mirror equation, which relates the object distance (u), image distance (v), and focal length (f) of a mirror:
1/f = 1/v + 1/u
Plugging in the given values, we get:
1/5 = 1/v + 1/15
Solving for v, we get v = 7.5 cm.
Now that we know the distance of the image from the mirror, we can use similar triangles to find the size of the image. The height of the image (h') is related to the height of the object (h) by the magnification equation:
h'/h = -v/u
where the negative sign indicates that the image is inverted. Plugging in the values we have, we get:
h'/4 = -(7.5/15)
Solving for h', we get h' = 2 cm.
Therefore, the size of the image is 2 cm.