Refraction of Light

3.2.2 Refraction of light

Refraction is the bending of light as it passes from one transparent medium to another. This bending occurs because the speed of light changes when it enters a different medium.

Key Terms

• Normal: A perpendicular line drawn to the surface at the point where the light ray strikes.
• Angle of Incidence: The angle between the incident ray and the normal.
• Angle of Refraction: The angle between the refracted ray and the normal.

Diagram

Mathematical Relationship

Snell's Law describes the relationship between the angles of incidence and refraction:

$$n_1 \sin{\theta_1} = n_2 \sin{\theta_2}$$

Where:

• $n_1$ is the refractive index of the first medium (e.g., air).
• $\theta_1$ is the angle of incidence.
• $n_2$ is the refractive index of the second medium (e.g., water).
• $\theta_2$ is the angle of refraction.

The refractive index ($n$) of a medium is defined as the ratio of the speed of light in a vacuum ($c$) to the speed of light in the medium ($v$):

$$n = \frac{c}{v}$$

The refractive index of a medium is always greater than or equal to 1. The refractive index of a vacuum is 1.

Examples

Scenario	Refractive Index of Medium 1	Angle of Incidence	Refractive Index of Medium 2	Angle of Refraction	Observation
Light from air to water	1.00	20°	1.33	48.6°	The light bends away from the normal.
Light from water to air	1.33	48.6°	1.00	20°	The light bends towards the normal.

Total Internal Reflection

Total internal reflection occurs when light travels from a denser medium to a less dense medium and the angle of incidence is greater than the critical angle. The critical angle ($\theta_c$) is the angle of incidence at which the angle of refraction is 90 degrees.

The critical angle can be calculated using the following formula:

$$\sin{\theta_c} = \frac{n_2}{n_1}$$

If the angle of incidence is greater than the critical angle, all the light is reflected back into the denser medium.