subroutine fresnelval(nopr,iout,nr,ni,coschi,sinchi,R1)
 
! **********************************************************
! to compute the Fresnel's coefficient of reflection (see for
! example M. Born and E. Wolf, Principles of Optics, Pergamon Press, fifth
! edition, 1975, pp 628
! input parameters: nr=index of refraction of the sea water
!                   ni=extinction coefficient of the sea water
!                   coschi & sinchi=cosine and sine of the incident radiation 
!                                   with respect of the wave facet normal.
! output parameter: R1=Fresnel's coefficient for reflection

! **********************************************************
 
      real :: a1,a2,u,v,Rr2,Rl2,b1,b2,R1,coschi,sinchi
      real :: nr,ni
      real :: vec(2)

! absolute value for a1 to get v=0 when ni=0
      a1=abs(nr*nr-ni*ni-sinchi*sinchi)
      a2=sqrt((nr*nr-ni*ni-sinchi*sinchi)**2.+4*nr*nr*ni*ni)
      u=sqrt(0.5*(a1+a2))
       vec(1)=0.0
       vec(2)=0.5*(-a1+a2)
       vdat=max(vec(1),vec(2))
      v=sqrt(vdat)
      Rr2=((coschi-u)**2+v*v)/((coschi+u)**2+v*v)
      b1=(nr*nr-ni*ni)*coschi
      b2=2*nr*ni*coschi
      Rl2=((b1-u)**2+(b2-v)**2)/((b1+u)**2+(b2+v)**2)

      R1=(Rr2+Rl2)/2.0

! ******
     if (nopr .eq. 1) then
      write(iout,100) nr,ni,coschi,sinchi,R1
      100 format(/,2x,'fresnelval: nr,ni,coschi,sinchi,R1',/,&
      2x,1p,5(1x,e12.5))
     endif

! ******
      return
      end