The conditions are determined under which the damping of the fast Alfve´n wave, used in the heating of tokamak plasmas, can be described by the geometrical optics approximations. Also, for these conditions, an analytic formula is derived, which explicitly determines the amount of energy that is damped onto the plasma particles by the fast wave. The conditions for the validity of the geometrical optics approximations cover a wide range ofk∥’s (the component of the wave vector parallel to the total magnetic field). There is a narrow range ofk∥’s over which this is not valid; this is the regime where mode conversion is dominant. The results from this theory are in good agreement with those obtained from numerical solutions of fourth‐ and sixth‐order differential equations that are commonly used to describe this type of heating. However, this theory has a distinct advantage of lending itself to detailed scaling studies as explicit expressions for the damping of the fast Alfve´n wave are obtained.