An object that is 3 cm tall is positioned at a distance of 7.5 cm from a convex mirror with a focal length of 6 cm . Determine the location, size, and nature of the image formed.

Step-by-step solution

Using the mirror formula, 1 v + 1 u = 1 f Given u = -7.5 cm and f = +6 cm for a convex mirror: 1 v = 1 6 - 1 -7.5 = 1 6 + 1 7.5 = 1 6 + 2 15 1 v = 5 + 4 30 = 9 30 = 3 10 v = 10 3 cm Since v is positive, the image is formed 10 3 cm behind the mirror. Magnification m = - v u = - 10 3 -7.5 = 10 3 7.5 = 10 22.5 = 4 9 Height of the image h_i = m h_o = 4 9 3 cm = 4 3 cm 1.33 cm Since m is positive, the image is virtual and erect.