Snell’s Law §

Introduction §

Snell’s Law, named after the Dutch astronomer Willebrord Snellius, is a fundamental principle in optics that describes the relationship between the angles of incidence and refraction when light passes through different media. This law is vital for understanding how light behaves when it moves from one material to another, such as from air into water or glass.

The Law §

Snell’s Law is mathematically expressed as:

$n_1\sin ({\theta }_1)=n_2\sin ({\theta }_2)$

where:

• $n_1$ and $n_2$ are the refractive indices of the first and second media, respectively.
• ${\theta }_1$ is the angle of incidence (the angle between the incident ray and the normal to the surface).
• ${\theta }_2$ is the angle of refraction (the angle between the refracted ray and the normal).

Application §

Snell’s Law is applied in various fields, including physics and engineering. It explains phenomena like the bending of light rays when entering a different medium, critical in designing lenses for glasses, cameras, and telescopes.

Historical Context §

The concept of refraction was first accurately described by Ibn Sahl in the 10th century and later by Snellius in 1621. Their work laid the foundation for the modern understanding of light behaviour in different media.

Examples §

1. Light entering water: When light rays from the air enter water, they slow down and bend towards the normal due to the higher refractive index of water.
2. Fiber optics: In fiber optics, light is transmitted through fibers using the principle of total internal reflection, a phenomenon explained by Snell’s Law.

Conclusion and Test Questions §

Understanding Snell’s Law is crucial for grasping the fundamental concepts of optics and light behaviour in different media.

Test Questions §

1. STARTI [Basic] Question: What does Snell’s Law mathematically relate? Back: Snell’s Law relates the angles of incidence and refraction to the refractive indices of two different media. ENDI
2. STARTI [Basic] Question: How does light change when moving from a medium with a lower refractive index to one with a higher refractive index? Back: When light moves from a medium with a lower refractive index to a higher one, it slows down and bends towards the normal. ENDI
3. STARTI [Basic] Question: If light enters water at an angle of incidence of 30 degrees and the refractive index of water is 1.33, what is the angle of refraction? (Use $n_1=1$ for air) Back: Using Snell’s Law, $\sin ({\theta }_2)=\frac{n_1}{n_2}\sin ({\theta }_1)=\frac{1}{1.33}\sin (30)$, which gives an angle of refraction ${\theta }_2$ approximately equal to 22.2 degrees. ENDI