Determine the diameter of the image of the moon produced by a spherical concave mirror having a focal length of 7.6 m . The moon's diameter is 3450 km and the distance between the earth and the moon is 3.8 10^5 km .

Step-by-step solution

Given, focal length of the mirror, f = 7.6 m Diameter of the moon, D_o = 3450 km = 3.45 10^6 m Distance of the moon from the mirror, u = 3.8 10^5 km = 3.8 10^8 m Since the moon is at a very large distance, its image is formed at the focus of the concave mirror. Image distance, v f = 7.6 m The angle subtended by the object at the pole of the mirror is equal to the angle subtended by the image at the pole. = D_o u = D_i v Substituting the values: 3.45 10^6 3.8 10^8 = D_i 7.6 D_i = 7.6 3.45 10^6 3.8 10^8 D_i = 2 3.45