What is refraction of light? Show by ray diagram how light bends when it travels from rare to denser medium and from denser to rare medium. Define the refractive index of a medium. What are its different formulae?

Refraction of Light:

Refraction is the bending of light as it passes from one medium to another due to a change in its speed. When light travels from a medium of one optical density to another, its speed changes, causing the light to bend. This bending of light is called refraction. The amount of bending depends on the angle at which the light strikes the surface between the two media and the refractive indices of the media involved.

Refractive Index of a Medium:

The refractive index (denoted by n) of a medium is a measure of how much the speed of light is reduced inside that medium compared to its speed in a vacuum.

It is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v):

n=c/v​

Where:

• n is the refractive index of the medium.
• c is the speed of light in a vacuum (3×108 m/s3 \times 10^8 \, \text{m/s}3×108m/s).
• v is the speed of light in the medium.

Different Formulae for Refractive Index:

1. Snell’s Law:

Snell’s Law gives the relationship between the angles of incidence and refraction in two media. It is expressed as:

sinθ1​​/sin⁡θ2=n1/​n2​​​​

Where:

• θ1 is the angle of incidence.
• θ2 is the angle of refraction.
• n1 is the refractive index of the first medium.
• n2 is the refractive index of the second medium.

2. Refractive Index Using Critical Angle:

The critical angle (θc) is the angle of incidence in the denser medium at which the angle of refraction in the rarer medium is 90° (i.e., the refracted ray runs along the boundary). The refractive index of the denser medium can be calculated using:

n=1/sin⁡θc​

Where θc is the critical angle.

Summary of Refraction:

• Refraction occurs due to the change in speed when light travels from one medium to another.
• Light bends towards the normal when it goes from a rarer to a denser medium and away from the normal when it goes from a denser to a rarer medium.
• The refractive index defines how much light slows down in a medium and is given by the formula n=cvn = \frac{c}{v}n=vc​.
• Snell’s Law relates the angles of incidence and refraction to the refractive indices of the two media.