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Question

Consider a 'beam expander' which consists of two converging lenses of focal lengths 40cm and 100cm having a common optical axis. A laser beam of diameter 2mm is incident on the 40cm focal length lens. Then what is the diameter (in mm) of the final beam (see figure)?


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Solution

Step 1: Given information

Diameter of the beam, 2r1=2mm

The focal length of lenses,

f1=40cmf2=100cm

Step 2: To find

The diameter of the final beam.

Step 3: Finding the diameter of the final beam

An objective lens plus an imaging lens together with a beam expander. As we've seen, the ratio of the first lens's radius and focal length is identical to the proportion of the second lens's radius and focal length.

Therefore,

r1f1=r2f2

By substituting the given values, we get

140=r2100r2=100402r2=5mmDiameter=5mm

Therefore, the diameter of the final beam will be 5mm.


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