# Refractometry, Snell's Law, Total Reflection

```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&lt;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&gt;n1)
From Snell’s formula we obtain that α&gt;β which means that the angle of refraction is less than the
ange of incidence.
When α=90ο =&gt; 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 =&gt; 𝑠𝑖𝑛 𝑏 = 𝑛2 ⋅ 𝑠𝑖𝑛 𝑎 =&gt; 𝑠𝑖𝑛 𝛽 = 𝑛2 ⋅ 𝑠𝑖𝑛 90 =&gt; 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&gt;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 -&gt; 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).
```