The figure below shows a beam expander made with two coaxial converging lenses o

Question

The figure below shows a beam expander made with two coaxial converging lenses of focal lengths f1 and f2 and separation d = f1 +f2. The device can expand a laser beam while keeping the light rays in the beam parallel to the central axis through the lenses. Suppose a uniform laser beam of width Wi = 2.6 mm and intensity Ii = 7.0 kW/m2 enters a beam expander for which f1 = 12.5 cm and f2 = 40.0 cm.

(a) What is Wf?

(b) What is If of the beam leaving the expander?

(c) What value of d is needed for the beam expander if lens 1 is replaced with a diverging lens of focal length f1 = 20.5cm?

Explanation / Answer

Part A)

The magnification is f2/f1 = 30/12.5

M = 3.2

Wf/Wi = 3.2

Wf = (3.2)(2.6) = 8.32 mm

Part B)

Intensity = P/A

7000 = (P)/(pi)(.0013)^2

P = .0037165 W

Then, for the second lens

I = (.0037165)/(pi)(.0036)^2

I = 91.28 W/m^2

Part C)

f = -22.5

d = (12.5 - 20.5) = -8 cm

The negative means that the diverging lens will be in front of the converging lens by 10 cm

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