Laws of Refraction

Refraction occurs when a light ray passes from one medium to another, causing it to bend due to a change in speed. The diagram illustrates light entering a glass slab from air.

• AN is the incident ray in air.
• NB is the refracted ray inside the glass slab.
• CD is the normal at the point of incidence N.

At N, the light bends following the laws of refraction.

Light ray entering a glass slab from air

Laws of Refraction:

1. The incident ray, refracted ray, and the normal at the point of incidence all lie in the same plane.
2. For a given pair of media (e.g., air and glass), the ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r) is constant.

This is mathematically expressed as : `"sin i"/"sin r"` = constant

This principle is known as Snell’s Law, named after Willebrord Snell, who discovered it. Snell’s Law relates the angles of incidence and refraction to the refractive indices of the two media. These laws explain why light bends at boundaries and are fundamental in optical physics, influencing the design of lenses, prisms, and optical instruments.

The refractive index measures how much a light ray bends when entering a different medium due to a change in speed. The refractive index of a medium depends on the velocity of light in that medium and is given by:

`n = "Speed of Light in Vacuum (c)"/"Speed of Light in Medium (v)"`

where:

• n = Refractive index of the medium
• c = Speed of light in a vacuum
• v = Speed of light in the given medium

Since the refractive index is inversely proportional to the velocity of light in a medium:

• Higher velocity → Lower refractive index (light travels faster).
• Lower velocity → Higher refractive index (light slows down).

If light moves between two different media, the refractive index is calculated as:

\[\mathrm{Refractive~index~^1n_2=\frac{Velocity~of~light~in~medium~1~(v_1)}{Velocity~of~light~in~medium~2~(v_2)}}\]

If one of the media is a vacuum, the refractive index of the second medium is called the absolute refractive index, denoted by n:

`n = "Speed of Light in Vacuum (c)"/"Speed of Light in Medium (v)"`

For example, the refractive index of water is 1.33, meaning light travels 1.33 times slower in water than in a vacuum.