A pin of length 2.00 cm is positioned perpendicular to the principal axis of a converging lens. An inverted image measuring 1.00 cm in size is produced at a distance of 40.0 cm from the pin. Determine the focal length of the lens and its distance from the pin.

Step-by-step solution

Given height of the object, h_o = 2.00 cm Height of the inverted image, h_i = -1.00 cm Distance between the object and the image, D = 40.0 cm Magnification of the lens is given by m = v u = h_i h_o v u = -1.00 2.00 = -0.5 v = -0.5u For a real image, the object and image are on opposite sides of the lens. The distance between them is v - u = 40.0 cm . Substituting v = -0.5u : -0.5u - u = 40.0 -1.5u = 40.0 u = - 80 3 -26.7 cm The distance of the lens from the pin is |u| = 26.7 cm . The image distance is v = -0.5 (- 8