A collimated beam of light of diameter 2 mm is propagating along $x$-axis. The beam is required to b

Question

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. If first lens has focal length 40 mm , then the focal length of second lens is $\_\_\_\_$ mm.

Professor PC Thomas Classes · Answer

To expand a collimated beam using two convex lenses, they must be arranged such that their focal points coincide (afocal configuration). The ratio of the diameters of the emergent and incident collimated beams is equal to the ratio of their focal lengths: $\frac{D_2}{D_1} = \frac{f_2}{f_1}$. Substituting the given values: $\frac{14 	ext{ mm}}{2 	ext{ mm}} = \frac{f_2}{40 	ext{ mm}} \Rightarrow 7 = \frac{f_2}{40} \Rightarrow f_2 = 280 	ext{ mm}$.