  Null geodesics are invariant under a conformal transformation, and thus it
might seem natural to assume that the observables corresponding to the shadow
of a space-time are also conformally invariant. Here, we argue instead, that
since the Arnowitt-Deser-Misner mass and the active gravitational mass of an
asymptotically flat space-time are not, in general, invariant under such
conformal transformations, the shadow radius for photon motion in a space-time
would be quantitatively different, when viewed from two different conformally
related frames, although the expression for the shadow radius is similar. We
then use this fact to propose a novel method to constrain the relevant
parameters in a gravity theory conformally related to general relativity. As
examples of our method, we constrain the parameter space in Brans-Dicke theory,
and a class of brane-world gravity models, by using the recent observational
data of M$87^{*}$ by the Event Horizon Telescope.
