Answer to Question #183876 in Optics for Michel

Question

a number of scientists between the 10th and the 17th centuries (sahl, snellius, descartes) concluded that the following formula should relate the angle of incidence with the angle of refraction. Sini= sinr/n explain?

Answer 1

Snell’s law gives the degree of refraction and relation between the angle of incidence, the angle of refraction and refractive indices of a given pair of media. We know that light experiences the refraction or bending when it travels from one medium to another medium. Snell’s law predicts the degree of the bend. It is also known as the law of refraction. In 1621, Willebrord Snell discovered the law of refraction, hence called Snell’s law.

Snell’s law is defined as “The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, for the light of a given color and for the given pair of media”. Snell’s law formula is expressed as:

$$\dfrac{sini}{sinr}=constant=\mu$$

Where i is the angle of incidence and r is the angle of refraction. This constant value is called the refractive index of the second medium with respect to the first.

The following is a diagrammatic representation:

Snell’s law formula is derived from Fermat’s principle. Fermat’s principle states that “light travels in the shortest path that takes the least time”.

$$n_1sin\theta_1=n_2sin\theta_2$$

The normal on the surface is used to gauge the angles that the refracted ray creates at the contact point. n1 and n2 are the two different mediums that will impact the refraction.θ1 is the angle of incidence; θ2 is the angle of refraction.