Linear water-wave theory is used to tackle the problem of diffraction
of surface waves by a fixed slender barrier in deep water for two basi
c situations: (i) when the barrier is partially immersed, and (ii) whe
n the barrier is completely submerged. Analytical expressions for the
first-order corrections to the reflection and transmission coefficient
s are derived in terms of integrals involving the shape functions desc
ribing the two sides of the slender barrier. A relatively straightforw
ard perturbation technique is used along with the application of Green
's theorem in the fluid region. Corresponding analytical expressions r
epresenting the reflection and transmission coefficients are also dedu
ced, (i) for a nearly vertical barrier and (ii) for a vertically symme
tric slender barrier, as special cases for both the problems. For a ne
arly vertical barrier it is observed, analytically, that there is no f
irst-order correction to the transmitted wave at any frequency. Comput
ations for the reflection and transmission coefficients up to O(epsilo
n), where epsilon is a Small nondimensional number, are also performed
and presented here.