 Optical biprism

An optical biprism combines two shallow prism regions that deflect parts of an incident beam in different directions. In the familiar Fresnel arrangement, associated with Augustin-Jean Fresnel, the regions act like two thin optical prisms placed base to base. Light from one narrow illuminated slit emerges as if from two separated virtual images of that slit. Where the two parts overlap, their optical coherence permits wave interference.^[ref]

This supplies two related optical sources without requiring two independent lamps to maintain a stable phase difference. A bench apparatus uses a narrow slit, the optical biprism, and a movable eyepiece or screen. A micrometer translation measures the spacing of several interference fringes. A convex lens can image the two virtual sources in either of two conjugate positions; if their measured image separations are $d_1,d_2$, their actual full separation is $d=\sqrt{d_1{d}_2}$. The inverse magnifications of the two positions explain the geometric mean.^[ref]

A thin-prism calculation makes the geometry explicit. Let each region have small wedge angle $\alpha$, refractive index $n$ relative to air, and slit-to-prism distance $a$. The paraxial deviation is $\delta \simeq (n-1)\alpha$. Backward extension of the emergent rays locates the virtual sources a distance $a\delta$ above and below the original slit, soAt a screen a further distance $b$ beyond the prism, the source-to-screen distance is $D=a+b$. Near the axis, the optical path difference is $dy/D$, giving interference fringe spacingThe symbols here use $d$ for the full source separation; the apparatus manual uses $2d$ for that same quantity.

For an original chosen model, $n=1.50$, $\alpha =1^{\circ }$, $a=0.10\mathrm{m}$, $b=0.90\mathrm{m}$ and $\lambda =600\mathrm{nm}$ give $d\simeq 1.745\mathrm{mm}$ and $\beta \simeq 0.344\mathrm{mm}$. The wedge angle must be converted to radians in the small-angle formula.

A finite slit width, limited optical coherence, unequal beam intensities and misalignment can reduce fringe visibility. The Wollaston prism instead separates linear polarization components using birefringence; its two beams do not automatically interfere on an ordinary intensity screen because their polarizations are orthogonal.