An object of height 2.5cm is places 20cm from a convex mirror of focal length 10cm. Calculate the height of its image.

Answer Details

The given problem is related to optics and involves the use of the mirror formula. According to the mirror formula, 1/f = 1/v + 1/u where, f = focal length of the mirror u = object distance v = image distance The magnification produced by the mirror is given by the ratio of the height of the image to the height of the object. magnification = height of image / height of object From the problem statement, height of object (h) = 2.5 cm distance of object from the mirror (u) = 20 cm focal length of the mirror (f) = 10 cm Using the mirror formula, we can find the image distance (v) as: 1/10 = 1/v + 1/20 => 1/v = 1/10 - 1/20 => v = 20 cm The image is formed at a distance of 20 cm from the mirror. Now, using the magnification formula, we can find the height of the image as: magnification = height of image / height of object => height of image = magnification * height of object The magnification produced by a convex mirror is always less than 1. Therefore, the image formed will be smaller than the object. For a convex mirror, magnification = -v/u Substituting the given values, we get: magnification = -20/20 = -1 Therefore, the height of the image is given by: height of image = magnification * height of object => height of image = -1 * 2.5 cm => height of image = -2.5 cm Since the height of the image cannot be negative, we take its absolute value: height of image = |-2.5 cm| = 2.5 cm Hence, the height of the image is 2.5 cm. Therefore, the correct option is (a) 2.5 cm.