Chapter 1: Refractometry Theoretical background Important to know: Light travels through a vacuum at a speed c = 3 x 10 8 m/s Light travels through materials at a speed less than its speed in a vacuum Always c1<c (Light’s highest speed is when travels in vacum) Also, the frequency of light does not changes only wavelength and speed does Refraction: When a beam of light strikes (hits) a boundary surface which separates two different transparent media, then the trasmitted ray changes its direction and becomes refracted. Law of light Refraction-Snell’s Law The ratio of the sine of the angle of incidence (α) to that of the angle of refraction equals ratio of the speed of light in the corresponding media 𝑐 sin 𝑎 𝑐1 𝑐2 𝑛2 = = 𝑐 = sin 𝛽 𝑐2 𝑛1 𝑐 n1, n2: indices of medium 1 and 2 Snell’s Law: The ratio of the sine of the angle of incidence (α) to that of angle of refraction (β) equals the relative index of the second medium. sin 𝑎 𝑛1 = = 𝑛21 sin 𝛽 𝑛1 Index of refraction: Absolute index of refraction (n1): the ratio of the speed of light in vacuum (c) to that in the medium (c1). It is given by the following formula: 𝑛1 = 𝐶 𝐶1 Relative index of refraction: the ratio of the speed of the indices of refraction of the two media. It is given by the formula: 𝑛21 = 𝑛2 𝑛1 Factors influencing the value of index of refraction (n): 1. Density of mean: n ∝ density (the refraction index is higher in denser means) nair= 1 nglass= 1.5 2. Frequency of light (thus λο) : Refraction index is slightly different for the diffent colors of light. 3. Temperature Critical angle:is the largest angle (βc) of refraction that corresponds to the grazing ray. A light beam propagates from a less dense medium towards the more dense one (n2>n1) From Snell’s formula we obtain that α>β which means that the angle of refraction is less than the ange of incidence. When α=90ο => grazing ray( grazing ray is a tangetial ray along the boundary of the two media) To estimate the critical angle we set α=90o sin 𝑎 sin 𝛽 𝑛 𝑛 1 𝑛 1 𝑛 = 𝑛1 1 => 𝑠𝑖𝑛 𝑏 = 𝑛2 ⋅ 𝑠𝑖𝑛 𝑎 => 𝑠𝑖𝑛 𝛽 = 𝑛2 ⋅ 𝑠𝑖𝑛 90 => sin 𝛽 = 𝑛2 1 1 1 1 Total Reflection or complete reflection (https://www.britannica.com/science/total-internal-reflection) When the incidence angle is larger than the critical angle the beam cannot propagate in the other mean thus, it returns back to the medium. This phenomenon can be seen only when the beam indices to a less densed mean. (n1>n2) Implementations: periscopes, telescopes, and other optical instruments. Snell Circle Snell’s window occurs when incident light rays from all directions enter at a point of the boundary surface from the less dense medium (e.g from air to water) This creates a bright light cone. Outside the light cone there is darkness. Apenture angle/2=critical angle Abbe-refractometer: Abbe refractometer is used to determine the index of refraction by measuring the shadowline position. The Abbee refractometer can be used t measure solutions with refraction index less than that of the prism. Working principle: The measuring prism of the Abbe refractometer is made of flint glass (n -> high). Between the prisms there is a narrow slim (0.1 mm) where the sample solution is dropped onto the rough surface of the illuminating prism. After placing the sample the prism is closed and the solution forms a thin film between the two prisms. In the refractometry viewfield we can only see a part of the shadowline. To estimate the index of refraction we turn the knob until the colors around the shadowline disapper (fig 1 and 2) and the shadowline gets sharp. We keep turn the knob until the sharpline is centered on the crossline (fig. 3).
