Pulfrich refractometer

Pulfrich refractometer (wood engraving 1897)

Schematic representation of the beam path in the Pulfrich refractometer

A Pulfrich refractometer is a type of refractometer that is named after Carl Pulfrich . It consists of a cuboid glass body with a known refractive index , a telescope and an option to read the angle between the cuboid and the telescope.

function

At the top, the glass cube is brought into contact with the test item. The interface is illuminated from the side with slightly convergent light. The part of the light bundle that falls from the side of the glass body onto the interface is passed on by total reflection in the glass body. The part of the light that falls from the side of the test object (refractive index ) onto the interface is refracted and transmitted. Due to the total reflection, a dark area arises between the transmitted and the totally reflected rays. Then all rays are refracted on the side surface. The angle between the interface normal and the beam that is just about to be refracted is determined with the telescope. This critical angle of total reflection is given by in the figure . If the telescope is now adjusted to the angle , the border crossing is manifested by a sharp light-dark transition. The critical angle is given by: ${\displaystyle n<n_{G}}$ ${\displaystyle \theta }$ ${\displaystyle \varphi }$

${\displaystyle \sin \theta ={\frac {n}{n_{G}}}}$

This ray is refracted on the side surface. The angle of incidence to the perpendicular for the exit angle (measured to the perpendicular) applies according to the law of refraction ${\displaystyle 90^{\circ }-\theta }$ ${\displaystyle \varphi }$

${\displaystyle {\frac {\sin(90^{\circ }-\theta )}{\sin \varphi }}={\frac {1}{n_{G}}}\Rightarrow \cos \theta ={\frac {\sin \varphi }{n_{G}}}}$

From the trigonometric identity it now follows: ${\displaystyle \sin ^{2}\theta +\cos ^{2}\theta =1}$

${\displaystyle n={\sqrt {n_{G}^{2}-\sin ^{2}\varphi }}}$

Application example

For example, the refractive index of ethanol can be determined with a Pulfrich refractometer. If a Pulfrich refractometer made of quartz glass with a refractive index is used , the measurement of the angle on the telescope results . The formula above gives: ${\displaystyle n_{G}=1{,}46}$ ${\displaystyle \varphi =31{,}83^{\circ }}$

${\displaystyle n={\sqrt {(1{,}46)^{2}-\sin ^{2}(31{,}83^{\circ })}}=1{,}361}$

Individual evidence

1. ↑ ^{a b} Clemens Schäfer: Optics: Wave and Particle Optics . Walter de Gruyter, 2004, ISBN 3-11-017081-7 , p. 70 ( limited preview in Google Book search).
2. ↑ Entry on ethanol. In: Römpp Online . Georg Thieme Verlag, accessed on November 11, 2011.