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

Question

The diameter of a laser beam is due entirely to the diameter of thehole 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 3.0 cm at a distance of 22.5 m. The wavelength ofthe 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 thecenter of the di?raction

pattern to the ?rst dark ring. Give the answer to 2 signi?cant?gures.

Explanation / Answer

Distance from hole D = 22.5 m wavelength = 633 nm = 633 * 10 ^ -9 m diameter of the beam at a distance 22.5 mis   y = 3 cm = 0.03 m Radius of the beam at a distance 22.5 m is  y ' = y / 2 = 0.015 m let the diameter of the hole be d then d sin =         d ( y ' / D ) =       Since for smallangles sin ~ tan ~ = y ' / D from this diameter of the hole   d = D /y '                                                   = 945.5 * 10 ^ -6 m                                                    =0.9455 * 10 ^ -3 m                                                   = 0.9455 mm

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