Light deflection angle through velocity profile of galaxies in $f(R)$
  model
  We explore a new realisation of the galactic scale dynamics via gravitational
lensing phenomenon in power-law $f(R)$ gravity theory of the type $f(R)\propto
R^{1+\delta}$ with $\delta<<1$ for interpreting the clustered dark matter
effects. We utilize the single effective point like potential (Newtonian
potential + $f(R)$ background potential) obtained under the weak field limit to
study the combined observations of galaxy rotation curve beyond the optical
disk size and their lensing profile in $f(R)$ frame work. We calculate the
magnitude of light deflection angle with the characteristic length scale
(because of Noether symmetry in $f(R)$ theories) appearing in the effective
$f(R)$ rotational velocity profile of a typical galaxy with the model parameter
$\delta \approx O(10^{-6})$ constrained in previous work. For instance, we work
with the two nearby controversial galaxies NGC 5533 and NGC 4138 and explore
their galactic features by analysing the lensing angle profiles in $f(R)$
background. We also contrast the magnitudes of $f(R)$ lensing angle profiles
and the relevant parameters of such galaxies with the generalised
pseudo-isothermal galaxy halo model and find consistency.
