What would be the total electric flux $\Phi_E$ through an infinite plane due to a point charge $q$ at a distance $d$ from the plane?

I think it should be ${q/2\epsilon_0}$ but I cannot justify that. My teacher says the flux is infinite due to the infinite area of the sheet which I cannot believe.

What would be the total electric flux $\Phi_E$ through an infinite plane due to a point charge $q$ at a distance $d$ from the plane?

I think it should be $\frac{q}{2\epsilon_0}$, but I cannot justify that. My teacher says the flux is infinite due to the infinite area of the sheet which I cannot believe.

What would be the total electric flux $\Phi_E$ through an infinite plane due to a point charge $q$ at a distance $d$ from the plane?

I think it should be ${q/2\epsilon_0}$ but I cannot justify that. My teacher says the flux is infinite due to the infinite area of the sheet which I cannot believe.

What would be the total electric flux $\Phi_E$ through an infinite plane due to a point charge $q$ at a distance $d$ from the plane?

I think it should be ${q/2\epsilon_0}$ but I cannot justify that. My teacher says the flux is infinite due to the infinite area of the sheet which I cannot believe.