A helium-neon laser ( = 633 nm) is built with a glass tube of inside diameter 1.

Question

A helium-neon laser ( = 633 nm) is built with a glass tube of inside diameter 1.0 mm, as shown in the figure(Figure 1) . One mirror is partially transmitting to allow the laser beam out. An electrical discharge in the tube causes it to glow like a neon light. From an optical perspective, the laser beam is a light wave that diffracts out through a 1.0-mm-diameter circular opening.

The angle 1 to the first minimum is called the divergence angle of a laser beam. What is the divergence angle of this laser beam? Express your answer to two significant figures and include the appropriate units.

What is the diameter (in mm) of the laser beam after it travels 3.5 m? Express your answer to two significant figures and include the appropriate units.

What is the diameter of the laser beam after it travels 1.5 km? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Considering the laser as an airy disc, theta = 1.22 lambda/a
theta = angle to the first minima, lambda = wavelength, a = aperture

1. theta-1 = 1.22*633*10^-9/1*10^-3 = 0.00077226 rad
2. dia = 2rtheta-1 = 2*(3.5)*theta-1 = 0.5.405 mm
3. dia = 2 r theta1 = 2.31678 m

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