FANDOM


Let us consider two stars located at(-L,h/2) and (-L,-h/2). Suppose we have an infinite screen at x=0. The light from the two stars will create a double slit diffraction pattern on the screen. The size of the central ridge is determined by the condition that the differences in optical paths should be comparable with the wavelength

$ \lambda \approx \sqrt{L^2 + \left(r+h/2 \right )^2} - \sqrt{L^2 + \left(r-h/2 \right )^2} \approx \frac{r h}{L} \Rightarrow r \approx \frac{L \lambda}{h} $

where we assumed $ L \gg r,h $ (this regime is often called the far field). For a telescope to resolve the two objects, the size of its aperture should be larger then the radius of the main diffraction ridge. By substituting $ h/R = \Delta \theta $, where $ \Delta \theta $ is the angular separation we obtain the diffraction limit

$ \Delta \theta > \frac{\lambda}{2 r} $.

A more rigorous derivation adds the prefactor 1.22 to the right hand side of this equation.