Show that a Gaussian beam with a waist w located at a distance d, from a lens with focal length f is transformed to a beam with a waist w, located at a distance d on the other side of the lens (Fig. P5.7) given by d = and or (d, -f) (d-f) + (w/2) 2 2 (T/)* - (TV/^)** af W2 +f 1 W1 [(d/f)-1]+ (zw/2f) 21-1/2 TEW () T (1) Hint: Use the ABCD formalism and require that a pure imaginary q, transform into a pure imaginary 92. Apply (1) to the case w = 0 and compare with lens formula (5.85) for positions of object and image. Assume that (zw/2) < (d, -) and explore the correction to 1/d, in the lens formula due to the fact that w + 0. When is the correction most important? W2 (2) Figure P5.7