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Refraction Formula

Light travels in a straight line. This fact is very common for all. But it is true on the condition that the light rays are travelling in the same medium, as it is having the same density throughout. But, when light enters from one see-through medium to another, then this will be no more in a straight line. This is because of the refraction of the light from one medium to another medium. This article will explain its concept with refraction formula and examples.

Concept of Refraction

When light strikes a smooth surface or barrier between two transparent materials, the light is partly reflected, and partly refracted.  Refraction is the bending of a light wave when it enters into a medium where its speed is different. The refraction of light happens when it passes from a fast medium to a slow medium. Then it will bend the light ray toward the normal to the boundary between the two media.

The amount of bending will depend on the indices of refraction of the two media. In other words, the alteration in the direction of light when it crosses through obliquely from one see-through medium to another is termed as refraction of light. Snell’s law is there to govern this phenomenon of light.

Refraction Formula

Source: en.wikipedia.org

A ray of light while travelling from the lower side of the stick passes from water into the air and gets refracted away from the normal. Another ray of light is getting refracted in another direction. When we produce these two rays backwards, then they appear to meet at a point nearer to the water surface. Due to this image formed in such a way will be a virtual image.

The first law of refraction says that the normal, the incident ray, and refracted ray at the point of incidence, all are lying on a similar plane. The second law of refraction provides a relationship between the angle of refraction and the angle of incidence. This second law of refraction is popular as Snell’s law of refraction. According to it the ratio of the sine of the angle of incidence to the sine of the angle of refraction will be a constant.

The Formula for Refraction:

Its formula is based on Snell’s law. If i is the angle of incidence and r is the angle of refraction then according to Snell’s law, we have,

\(\frac{sin\;i}{sin\;r}=constant=\mu\)

This value is termed as the refractive index of the second medium with respect to the first medium. The index of refraction of a material depends on the material’s properties.

Also, another formula is:

\(n_{1} sin \theta_{1}=n_{2} sin \theta_{2}\)

Where refractive indices of medium-1 and medium-2 are \(n_{1}\) and \(n_{2}\)  respectively. Light enters from medium-1 to medium-2. Here, \(\theta_{1}\) is the angle of incidence and \(\theta_{2}\) is the angle of refraction. These angles are in the unit of radians or degrees. And the indexes of refraction are unitless numbers.

Solved Examples for Refraction Formula

Q.1: If the angle of incidence is 45° and angle of refraction is 60°. Determine the refractive index of the media using the refraction formula.

Solution: Given parameters in the problem is:

The angle of incidence, i = 45°

Angle of refraction, r = 60°

Using Snell’s law formula, we have:

\(\frac {sin\;i} {sin\;r} = \mu\)

Substituting the values of both angles.

\(\frac{sin45^{\circ}}{sin60^{\circ}}=\mu\)

\(\frac{0.70}{0.86}=\mu\)

\(\mu =0.81\)

Therefore, the refractive index of the media will be 0.81.

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