A concave mirror produces an image of a 20 cm high object on a screen located 5.0 m from the mirror. The height of the image is 50 cm . Determine the focal length of the mirror and the distance between the mirror and the object.

Step-by-step solution

Given that the image is formed on a screen, it is a real and inverted image. Height of the object, h_o = 20 cm = 0.2 m Height of the image, h_i = -50 cm = -0.5 m Image distance, v = -5.0 m Magnification, m = h_i h_o = -0.5 0.2 = -2.5 Using the relation m = - v u : -2.5 = - -5.0 u u = -2.0 m The distance between the mirror and the object is 2.0 m . Using the mirror formula 1 f = 1 v + 1 u : 1 f = 1 -5.0 + 1 -2.0 = -0.2 - 0.5 = -0.7 m ⁻¹ f = - 1 0.7 -1.43 m The focal length of the mirror is 1.43 m .