The Fresnel Bi-prism is a variation on the Young’s Slits experiment. A bi-prism is an (isosceles) triangular prism with an extremely low prism angle, typically made by joining two thin prisms at the base. A slit has a finite width which gives rise to unwanted diffraction effects causing errors. The Fresnel bi-prism overcomes this problem of extended secondary slits by replacing them with virtual slits which are point-like. A single wavefront impinges on both constituent prisms; the left portion of the wavefront is refracted right while the right segment is refracted left, creating the two virtual sources. Interference occurs in the region of superposition.

As this experiment is analogous to Young slits, Young’s formula holds. But since\(d\)cannot be measured directly as the two slits are purely virtual, it is determined instead by the ‘displacement method’. A converging lens is placed between the bi-prism and the eyepiece. It can be observed that the virtual image of the slit is formed at two locations (Figure 3), one diminished and one magnified. Measuring the slit distance in the two cases as \(d_2\) and \(d_1\) respectively and using the magnification formula we have, $$m_1=\frac{v_1}{u_1}=\frac{d_1}{d} \quad m_2= \frac{u_2}{v_2}= \frac{d_2}{d}$$ Since \( m_1m_2=1\) and \( u_1=v_2 \), we have \(d=\sqrt{d_2d_1} \) Putting this into Young’s formula, we get $$ \lambda = \frac{\beta \sqrt{d_2d_1}}{D}$$