  We study the sensitivity of $ e \gamma$ colliders to physics beyond the
Standard Model, when such interactions are natural and their scale lies below
the collider energy. Using the reaction $ e \gamma \to b t \nu$ as a specific
example, we show that the deviations from the Standard Model can be
parameterized in a model independent way by only 3 numbers. We investigate the
sensitivity of several observables to these 3 quantities, using the various
collider polarization modes to increase the signal to noise ratio. These
results are then translated into the expected sensitivity derived from this
reaction to the new physics effects present in several specific models.
