Question

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

Hint:

For beam expanders, diameter ratio = focal length ratio.

Answer 1

Correct Answer: 280

Step 1: Beam Expander Principle:
A beam expander composed of two convex lenses (Keplerian telescope) takes a collimated input beam and produces a larger collimated output beam. The lenses are separated by the sum of their focal lengths. Step 2: Formula:
The magnification of the beam diameter is equal to the ratio of the focal lengths of the output lens to the input lens. \[ M = \frac{D_{out}}{D_{in}} = \frac{f_2}{f_1} \] Step 3: Calculation:
Given: \(D_{in} = 2\) mm, \(D_{out} = 14\) mm, \(f_1 = 40\) mm. \[ \frac{14}{2} = \frac{f_2}{40} \] \[ 7 = \frac{f_2}{40} \] \[ f_2 = 280 \, \text{mm} \] Step 4: Final Answer:
280