An object is placed far beyond the centre of curvature of a concave mirror. The object then starts accelerating towards the mirror. Which one of the following is correct?

Step-by-step solution

Using the mirror formula: 1 v + 1 u = 1 f Differentiating with respect to time t , we get the velocity of the image v_i in terms of the velocity of the object v_o : - 1 v^2 dv dt - 1 u^2 du dt = 0 v_i = - ( v u )^2 v_o = - f^2 (u-f)^2 v_o Since the object is moving towards the mirror, u is increasing (becoming less negative), so v_o > 0 . This makes v_i To find the acceleration of the image a_i , we differentiate v_i with respect to t : a_i = dv_i dt = - f^2 (u-f)^2 a_o + 2f^2 (u-f)^3 v_o^2 Here, a_o > 0 because th