A helium-neon laser (lambda = 633 nm) is built with a glass tube of inside diame

Question

A helium-neon laser (lambda = 633 nm) is built with a glass tube of inside diameter 1.0 mm, as shown below. 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 output power of the laser is 1.5 mW. a. Can a laser beam be perfectly parallel, with no spreading? Make sure to explain your reasoning. b. The angle theta_1, to the first minimum is called the divergence angle of a laser beam. What is the divergence angle of this laser beam? c. What is the diameter (in mm) of the laser beam after it travels 4.9 m? d. Assuming no loss of power, what is the intensity at this distance? e. What is the diameter of the laser beam after it travels 1.3 km? f. If the moon is directly above you, what is the diameter of the laser beam on the surface of the moon? g. Assuming no loss of power, what is the intensity of the light on the surface of the moon? Is this visible to the naked eye?

Explanation / Answer

a) The waves in laser light are not parallel. It is theoretically impossible to construct a beam with perfectly parallel rays unless you have an infinitely wide beam. As described in the textbook “Principles of Lasers” by Orazio Svelto, even a perfectly spatially coherent beam will spread out due to diffraction

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

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

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