A candle flame 1.6 cm high is imaged in a ball bearing of diameter 0.4 cm . If the ball bearing is 20 cm away from the flame, determine the location and the height of the image.

Step-by-step solution

The ball bearing acts as a convex mirror. Radius of curvature R = 0.4 2 = 0.2 cm . Focal length f = R 2 = +0.1 cm . Object distance u = -20 cm . Using the mirror formula: 1 v + 1 u = 1 f 1 v - 1 20 = 1 0.1 = 10 1 v = 10 + 1 20 = 201 20 v = 20 201 cm 0.1 cm = 1.0 mm Since v > 0 , the image is virtual and formed 1.0 mm inside the ball bearing. Magnification m = - v u m = - 20/201 -20 = 1 201 Height of the image h_i = m h_o h_i = 1 201 1.6 cm 1.6 200 cm = 0.008 cm = 0.08 mm