(a) A luminous point is moving at speed v0 toward a spherical mirror with radius of curvature r, along the central axis of the mirror. Show that the image of this point is moving at speed v1 = – (r/2p – r)2 v0, where p is the distance of the luminous point from the mirror at any given time. Now assume the mirror is concave, with r = 15 cm, and let v0 = 5.0 cm/s. Find v1 when

(b) p = 30 cm (far outside the focal point),

(c) p = 8.0 cm (just outside the focal point), and

(d) p = 10 mm (very near the mirror).