A collimated beam of light of diameter 2 mm is propagating along x-axis. The beam is required to be expanded in a collimated beam of diameter 14 mm using a system of two convex lenses. lf first lens has focal length 40 mm, then the focal length of second lens is ____ mm.

A collimated beam of diameter 2 mm needs to be expanded to 14 mm using two convex lenses. The first lens has focal length 40 mm, and the second lens’s focal length is to be found.

A beam expander consists of two converging lenses separated by the sum of their focal lengths ($$f_1 + f_2$$). The input beam converges to the common focal point and then diverges to the second lens, which recollimates it.

The angular magnification (which equals the beam diameter ratio) of a beam expander is $$ M = \frac{d_2}{d_1} = \frac{f_2}{f_1} $$.

Substituting the given values gives $$ \frac{14}{2} = \frac{f_2}{40} $$.

This simplifies to $$7 = \frac{f_2}{40}$$, hence $$f_2 = 280 \text{ mm}$$.

The focal length of the second lens is $$\boxed{280}$$ mm.