Short Answer

Snell’s law is a rule that explains how light bends when it passes from one medium to another, such as from air to water or from air to glass. It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is always constant for the same pair of media. This constant is called the refractive index.

Snell’s law helps us calculate how much light will bend and in which direction. It is used in studying lenses, prisms, optical fibres, and many natural phenomena like rainbows and mirages.

Detailed Explanation :

Snell’s Law

Snell’s law is a fundamental law in optics that describes the behaviour of light as it travels from one transparent medium to another. When light passes from one medium into another—such as from air to water—it changes its speed. This change in speed causes the light to bend, a process known as refraction. Snell’s law helps us calculate this bending accurately.

This law was discovered by Willebrord Snell, a Dutch mathematician, in the 17th century. It forms the basis of many optical devices and plays a major role in understanding how lenses and prisms work.

Statement of Snell’s Law

Snell’s law states that:

The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for the same pair of media.

Mathematically, it is written as:

sin i / sin r = constant = refractive index (μ)

Where:

• i is the angle of incidence
• r is the angle of refraction
• μ is the refractive index of the second medium with respect to the first

This constant value changes only when the mediums change. For example, the value is different for air-to-water refraction and air-to-glass refraction.

Why Snell’s Law Works

When light enters a new medium, its speed changes because different materials have different optical densities. Light slows down when entering denser mediums like water or glass. It speeds up when entering less dense mediums like air.

Snell’s law is based on the relationship between:

• Speed of light in medium 1
• Speed of light in medium 2
• Angle at which the light bends

The refractive index is directly linked to this speed change. A higher refractive index means light slows down more and bends more.

Explanation of Refraction Using Snell’s Law

Snell’s law helps explain the behaviour of light during refraction:

1. From rarer to denser medium (e.g., air to water):
   Light slows down and bends towards the normal.
   This means the angle of refraction is smaller than the angle of incidence.
2. From denser to rarer medium (e.g., water to air):
   Light speeds up and bends away from the normal.
   This means the angle of refraction is larger than the angle of incidence.

Snell’s law quantifies these changes using the refractive index.

Refractive Index and Snell’s Law

The refractive index (μ) is a number that shows how much light bends when entering a medium. It is connected to Snell’s law through the formula:

μ = sin i / sin r

or
μ = speed of light in vacuum / speed of light in medium

Materials with high refractive index values, like glass and diamond, bend light more strongly. Materials like air have very low refractive indices and bend light very slightly.

Applications of Snell’s Law

Snell’s law is used widely in science and technology:

1. Lenses
   Convex and concave lenses work based on refraction. Snell’s law helps calculate focal points and image positions.
2. Optical Fibres
   Snell’s law explains how light remains trapped inside a fibre using total internal reflection, enabling fast communication.
3. Prism Design
   Prisms bend and split light. Engineers use Snell’s law to design prisms for cameras, binoculars, and laboratories.
4. Corrective Eyeglasses
   Lenses for spectacles are designed using refractive index values obtained through Snell’s law.
5. Cameras and Microscopes
   Snell’s law helps determine how light will behave as it passes through lenses in these devices.
6. Rainbows
   Light refracts inside raindrops, forming colourful rainbows due to bending at different angles.
7. Mirages
   In deserts and on hot roads, varying air densities cause refraction, creating the illusion of water.

Examples Showing Snell’s Law

Example 1: Bent Pencil in Water
A pencil dipped in water appears bent because light rays refract. Snell’s law explains why the angle of refraction changes inside water.

Example 2: Swimming Pool Appears Shallower
Objects under water appear raised because of refraction. Snell’s law tells us how much the image shifts.

Example 3: Spectacles Using High-Refractive-Index Lenses
Thinner lenses can be made using materials with high refractive indices, based on Snell’s law.

Importance of Snell’s Law

Snell’s law is essential because:

• It predicts the exact bending of light
• It helps design precise optical instruments
• It explains many natural phenomena
• It connects refractive index, speed of light, and angles of rays
• It provides a mathematical foundation for understanding lenses and prisms

Without Snell’s law, studying optics would be incomplete.

Conclusion

Snell’s law describes the relationship between the angles of incidence and refraction when light passes from one medium to another. It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction remains constant for a given pair of media. This constant is the refractive index. Snell’s law is fundamental in optics and helps explain image formation, lens behaviour, optical fibres, and many natural effects.