Chapter 34, Problem 31P

(a) A luminous point is moving at speed vo towards 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

$v_1=-{\left(\frac{r}{2p-r}\right)}^2{v}_O,$

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 vo = 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).