For two different photosensitive materials having work function $\phi$ and $2 \phi$ respectively, are illuminated with light of sufficient energy to emit electrons. If the graph of stopping potential versus frequency is drawn, for these two different photosensitive materials, the ratio of slope of graph for these two materials is

The photoelectric equation is given by $h\nu = \phi + eV_s$, where $h$ is Planck's constant, $\nu$ is the frequency of the incident light, $\phi$ is the work function, $e$ is the charge of an electron, and $V_s$ is the stopping potential.

Rearranging yields $eV_s = h\nu - \phi$, so $V_s = \frac{h}{e}\nu - \frac{\phi}{e}$, which is linear in $\nu$ with slope $m = \frac{h}{e}$.

Since $h$ and $e$ are fundamental constants, the slope $\frac{h}{e}$ remains the same for all photosensitive materials, regardless of their work function.

The ratio of slopes for any two materials is $1:1$.

Thus, the correct option is A.