Using Modern Physics for Scientists and Engineers (2nd) step-by-step solutions:

Question

Using Modern Physics for Scientists and Engineers (2nd) step-by-step solutions: Chapter 11 by John R. Taylor - Chapter 11 Question 32:

I am sorry to inconvenience again, but I am also stuck on Question 32:

32) A single-mode He-Ne laser has a beam diameter of 3 mm. As the beam propagates away from the laser, its diameter increases because of diffraction. (a) Given that this effect simply adds to the initial beam size, find the distance at which the beam diameter is doubled. (b) At what distance will the beam have a diameter of 1 m?

Explanation / Answer

radius of the beam at a distance L

              R = L / d

             d' / 2   = L / d  

where   = wave length f He neon laser

              d = initial diameter of the laser

distance at which the beam diameter is doubled   

               d' = 2 d

                d = L / d

            L = d^2 /

               = 9*10^ -6 / 633 *10^ -9 m

               = 14.2 m

distance at which the beam diameter is 1m

            1 m = L ( 633*10^ -9 ) / (3*10^ -3 )

               L =   4.739*10^ 3 m    

          

                          

             

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