What are n₁ and n₂?

They are the refractive indices of the two media through which light travels.

What happens when n₁ < n₂?

The ray bends toward the normal when entering the denser medium.

What is the critical angle?

It is the angle of incidence at which light is refracted at 90°, leading to total internal reflection beyond that angle.

Does Snell’s Law apply to sound?

Yes, any type of wave that changes speed across a boundary follows a similar relationship.

Why does a straw look bent in water?

Because of refraction—the light bends as it moves from water to air, displacing the straw’s image.

Different wavelengths of light refract by slightly different amounts, causing white light to spread into colors.

Can refractive index be less than 1?

Yes, in special materials like metamaterials or plasmas, but not in ordinary transparent substances.

Who discovered Snell’s Law?

It was formulated by Willebrord Snellius in 1621, though earlier observations existed.

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Understanding Snell’s Law

Snell’s Law, also called the Law of Refraction, describes how light changes direction when it moves between two transparent materials of different refractive indices. This principle is fundamental to optics, governing how lenses focus light, how prisms disperse colors, and how technologies like fiber optics transmit information. Without Snell’s Law, our understanding of vision, microscopy, and modern communication systems would be incomplete.

Mathematical Expression

n₁ sinθ₁ = n₂ sinθ₂

Where:

n₁ = refractive index of the first medium
θ₁ = angle of incidence (angle between incoming ray and the normal)
n₂ = refractive index of the second medium
θ₂ = angle of refraction (angle between refracted ray and the normal)

Refractive Index

The refractive index of a medium measures how much it slows down light relative to a vacuum. For example:

Air: ~1.0003
Water: ~1.33
Glass: 1.5–1.9 depending on type
Diamond: ~2.42

The greater the refractive index, the more light bends toward the normal when entering that medium.

History

The law is named after Willebrord Snellius (1580–1626), a Dutch astronomer and mathematician who formulated the relationship between incidence and refraction in 1621. However, ancient civilizations like the Greeks and Arabs observed refraction phenomena long before. Today, Snell’s Law remains one of the cornerstones of wave physics.

Applications

Lenses: Cameras, glasses, and microscopes rely on refraction for focusing images.
Prisms: Separate white light into the visible spectrum using refraction and dispersion.
Fiber Optics: Depend on total internal reflection (a consequence of Snell’s Law) for data transmission.
Vision Science: Explains why objects under water appear displaced.
Astronomy: Helps correct telescope lenses to reduce chromatic aberration.

Total Internal Reflection

When light passes from a denser medium (higher refractive index) to a rarer one (lower refractive index), there exists a critical angle at which refraction becomes impossible, and light reflects entirely inside the medium. This is called total internal reflection, the principle that enables fiber optic cables and sparkling effects in diamonds.

Worked Example

Suppose a ray of light enters water (n₁ = 1.00 for air, n₂ = 1.33 for water) at an incidence angle θ₁ = 30°. Using Snell’s Law:

sinθ₂ = (n₁ / n₂) × sinθ₁ = (1.00 / 1.33) × sin30° ≈ 0.376

Thus, θ₂ ≈ 22°. The ray bends toward the normal.

Beyond Light

Snell’s Law applies not just to visible light but also to sound waves, seismic waves, and even matter waves in quantum mechanics. Whenever a wave crosses a boundary where speed changes, refraction occurs according to Snell’s Law.

Conclusion

Snell’s Law is a universal principle that unites geometry, physics, and engineering. From eyeglasses to advanced optical networks, its applications shape daily life and cutting-edge science. By understanding and applying Snell’s Law, we gain insight into both the beauty of nature and the foundations of modern technology.

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