6.2.2. Refraction of Light

• Laws of Refraction (Snell’s Law):

$n_1 \sin i = n_2 \sin r$

Snell's Law describes how light bends when it passes from one medium to another. The formula states that the product of the refractive index of the first medium (n1) and the sine of the angle of incidence (i) equals the product of the refractive index of the second medium (n2) and the sine of the angle of refraction (r). This relationship helps us predict how much light will bend when entering a new material, for example, from air into water.

Imagine you're at the beach, and you stick your foot into the water. The way the water bends the light makes it look like your foot is at a different position. This bending happens because of refraction, where light travels at different speeds in air and water.

• Refractive Index (μ):

$\mu = \frac{\sin i}{\sin r}$

The refractive index (μ) is a dimensionless number that indicates how much light slows down in a medium compared to its speed in a vacuum. It is calculated by taking the ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r). If a medium has a higher refractive index, it means light travels slower in that medium, leading to more bending of light as it enters.

Think of light traveling through different materials like a car driving on various roads. If the road is smooth (like air), the car moves quickly. But on a bumpy road (like glass or water), the car slows down and changes direction more sharply—showing how light behaves in different media.

• Total Internal Reflection (TIR):

• Occurs when light travels from a denser to a rarer medium.
• Critical Angle: The angle of incidence for which the angle of refraction is 90°.
• Applications: Optical fibers, mirage, diamond sparkle.

Total Internal Reflection occurs when light attempts to move from a denser medium (like water) to a rarer medium (like air) and exceeds a certain angle, called the critical angle. Beyond this angle, all light is reflected back into the denser medium instead of passing through, which is why optical fibers can carry light over long distances without losing it. This phenomenon is also what causes the sparkling effects in diamonds and the visual illusions known as mirages.

Picture a swimmer diving underwater. When they try to look up at the sky at a steep angle, instead of seeing the sky, they see their own reflection on the water's surface. This happens because the light reflects back into the water when it hits the surface at a steep angle, demonstrating total internal reflection like light in optical fibers.

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