A particle travels in a circle of radius 2.0 cm . A concave mirror having a focal length of 20 cm is positioned so that its principal axis passes through the centre of the circle and is perpendicular to its plane. The distance from the pole of the mirror to the centre of the circle is 30 cm . Determine the radius of the circle traced by the image.

Step-by-step solution

Using the mirror formula, 1 v + 1 u = 1 f Given u = -30 cm and f = -20 cm 1 v = 1 -20 - 1 -30 = -3 + 2 60 = - 1 60 v = -60 cm The transverse magnification is given by m = - v u m = - -60 -30 = -2 The radius of the circle traced by the image is the transverse height of the image. R_ image = |m| R_ object R_ image = |-2| 2.0 cm = 4.0 cm