A smooth, silvered spherical surface acts as a convex mirror for light coming from the left.
(i) Draw a neat, labelled ray diagram showing an object at distance u on the left of the pole P of the mirror. Indicate the centre of curvature C, focal point F and image position I obtained by back-tracing the reflected rays.
(ii) Using only geometrical relations arising from the diagram and the Cartesian sign convention, obtain an algebraic expression that reduces to
v1+u1=f1
for the convex mirror.
(iii) Show further that the linear magnification produced by the mirror may be written as
m=−uv.