  We estimate the UV continuum slope ($\beta$) of 465 galaxies (with
luminosities of 0.028 $-$ 3.3 $L^{*}_{z=0.5}$) in the Great Observatories
Origins Survey (GOODS) Northern field in the redshift range $z=0.40 - 0.75$. We
use two AstroSat/UVIT (N242W, N245M), two HST (F275W, F336W), and a KPNO (U)
bands to sample the UV continuum slope of selected galaxies between 1215 and
2600 angstrom. The mean (median) and 1$\sigma$ scatter in the observed $\beta$
are found to be $-1.33\pm0.07~(-1.32)$ and 0.60 within the considered redshift
range. We do not find any significant evolution in the mean $\beta$ within our
redshift window. Our measurements add new data points to the global $\beta$ -
$z$ relation in the least-explored redshift regime, further reinforcing the
gradual reddening of galaxy UV continuum with cosmic time. We notice no strong
consistent trend between $\beta$ and M$_{1500}$ for the entire luminosity range
$-21$ $< M_{1500} <-15$ mag. Although, the majority of the most luminous
galaxies (M$_{1500} <-19$ mag) are found to have relatively redder slopes.
Using UVIT, we detect galaxies as faint as M$_{1500} = -15.6$ mag (i.e., 0.028
$L^{*}_{z=0.5}$). The faintest galaxies (M$_{1500} > -16$ mag) tend to be
redder, which indicates they were less actively forming stars during this
cosmic time interval. Our study highlights the unique capability of UVIT
near-UV imaging to characterize the rest-frame far-UV properties of galaxies at
redshift $z \sim 0.5$.
