A blue green laser is being tested as an experimental aircraft to submerged subm

Question

A blue green laser is being tested as an experimental aircraft to submerged submarine communication systems. Given the laser operates at a wavelength of 490 nm and is incident at an angle of 30.0 degrees to the normal to the ocean surface, and if the index of refraction in seawater is 1.33, a) if the submarine is at a submerged postion at an angle of 20 degrees to the normal to the ocean surface and in the same plane with respect to the aircraft can communication be established knowing the laser beam is very narrow (<1 degree)? b) What is the refracted wavelength? c) what is the speed of the laser beam in seawater? d) what is the frequency of this laser transmitted by the aircraft? e)if the communication receiver on the submarine is tuned to this frequency given it is in the beam, will it receive these laser signals?

Explanation / Answer

Given  wave length of  laser    =  490 nm  angle  of  incidence  of laser light     1  =  30 o  refractive  index  of sea water  n 2   = 1.33  angle  of  refracted  light  in sea  water is calculated by snells law            n 1 sin 1  = n 2  sin2                   sin 2   =   n1 sin1  / n 2                               =  sin 30  / 1.33                         2  = 22.0824 o here the submarine is at a submerged postion at an angle of 20 degrees to the normal to the ocean surface .  but the angle  of refracted  light  is  22o .so he communiation cannot  be established .  b)  wave  length of  ligth in sea water is               '  =    / n 2                   =  490 nm  / 1.33                   = 368.421 nm  c)   speed  of  light  in sea water                  v  = c  / n                      = ( 3*108 m/s )  / 1.33                     = 2.255 *108  m/s                       = 0.751 c       where  c  is speed  of light  d)   frequency of  laser transmitted by air craft               f  =  c  /                    =  ( 3*108  ) / ( 490 nm )                     = 6.122*1014   Hz  here the submarine is at a submerged postion at an angle of 20 degrees to the normal to the ocean surface .  but the angle  of refracted  light  is  22o .so he communiation cannot  be established .  b)  wave  length of  ligth in sea water is               '  =    / n 2                   =  490 nm  / 1.33                   = 368.421 nm  c)   speed  of  light  in sea water                  v  = c  / n                      = ( 3*108 m/s )  / 1.33                     = 2.255 *108  m/s                       = 0.751 c       where  c  is speed  of light  d)   frequency of  laser transmitted by air craft               f  =  c  /                    =  ( 3*108  ) / ( 490 nm )                     = 6.122*1014   Hz 

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