Snell's Law: The Law of Refraction

Snell's law, also known as the Snell-Descartes law, relates the incidence and refraction angles to the refraction indices of the media involved. As shown in the figure, the law determines that the product of the sine of the angle formed between the ray of light (1), the normal straight line (2) and the refractive index of the media (n₁ and n₂) must be constant.

n₁   sinα = n₂   sin⁡β

The figure shows how a light beam (1, blue arrow) is deflected when it crosses at a certain angle from an optically less dense (n₁) to an optically more dense medium (n₂), e.g. from air to water.

But when the beam crosses from one medium to another perpendicular to the dotted line, no directional change takes place (green arrow).

Snell's law states that the ratio of the refractive index of each of the media is proportional to the ratio of the incident and refractive angle of the light beam. Therefore:
 

Total internal reflection is defined as a process whereby all light traveling from an optically more dense medium towards an optically less dense one is reflected back into the optically more dense medium. Here is a detailed explanation of this phenomenon using the figure at left.

The dark blue line: If a light beam passes from an optically more dense (n₂) to an optically less dense medium (n₁), it is deflected.

From the dark blue to the green line: If the angle of incidence α is increased, then it can reach a critical value (1) at which the light beam no longer enters the less dense medium (n₁) and is instead refracted exactly along the interface of the two media. The angle (1) is known as the critical angle of total internal reflection. Note that the refractive angle β  = 90°.

From the green to the light blue line: When the critical angle is exceeded, all light is reflected back into the optically more dense medium (n₂). This is known as total internal reflection (2).

The refractive index n1 is calculated from this critical angle α:
β  = 90° —> sin β  = 1 

Remember: 1 (green) is the critical angle, and 2 (light blue) is the total internal reflection.

Using Snell’s Law, scientists engineered refractometers capable of accurately measuring the refractive index of both liquids and semi-solid samples. The accompanying schematic shows this mechanism in action.

When measuring refractive index:

1. A light-emitting diode or LED serves as the light source and emits a light beam. The LED beam that is emitted then passes through:
2. The polarization filter,
3. The interference filter, and
4. The focal lens. After filtering, the LED beam then reaches:
5. The sample held by the sapphire prism.
   
   Because the angle of incidence is greater than the critical angle:
   
   
6. Light is reflected and deflected via a lens in the sapphire prism to
7. The optical CCD sensor, which measures the critical angle.

Additionally, a modern digital refractometer controls the temperature at the prism/sample boundary automatically, further enhancing measurement accuracy.

Learn more about the definition, applications, how to measure it and much more.

Did you know that insufficient cleaning of the prism can falsify your next measurement?

Do you know which samples can be measured with a refractometer?

This guide explains what precautions should be taken to avoid errors when measuring the refractive index, BRIX, HFCS or concentration of liquids. Download our free guide.