The diameter of a laser beam is due entirely to the diameter of the hole through

Question

The diameter of a laser beam is due entirely to the diameter of the hole through which it passes as it exits the instrument. However, at large distances, thediameter of the beam increases due to diffraction at that hole. Suppose that for aparticular laser, the diameter of the beam is 1.6 cm at a distance of 22.5 m. The wavelength of the laser light is 633 nm. Find the diameter (mm) of the hole through whichthe beam exits the instrument. Caution: the value of ?min is measured from the center of the difraction pattern to the first dark ring. Give the answer to 2 significant figures.

Explanation / Answer

we know the first minimum occurs when sin() = 1.22/d. Solving for d,

d = 1.22/sin()

= (1.22)(633 * 10-9 m)/((0.008 m)/(22.5 m))

= 2.17 * 10-3 m or 2.2 mm

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