Refraction of Light

Objective

Recall and use the equation $n = \frac{\sin i}{\sin r}$

What is Refraction?

Refraction is the bending of light as it passes from one transparent medium to another. This bending occurs because light travels at different speeds in different media.

When light moves from a less dense medium (e.g., air) to a more dense medium (e.g., water), it bends towards the normal. When light moves from a more dense medium to a less dense medium, it bends away from the normal.

The Refraction Equation

The relationship between the angles of incidence (i) and refraction (r) and the refractive indices of the two media is given by Snell's Law, which can be expressed as:

$$n_1 \sin i = n_2 \sin r$$

Where:

• $n_1$ is the refractive index of the first medium.
• $i$ is the angle of incidence (the angle between the incident ray and the normal).
• $n_2$ is the refractive index of the second medium.
• $r$ is the angle of refraction (the angle between the refracted ray and the normal).

A common case is when light travels from air to water. The refractive index of air is approximately 1.00, and the refractive index of water is approximately 1.33. In this case, the equation simplifies to:

$$1.00 \sin i = 1.33 \sin r$$

Therefore, $r = \sin^{-1} \left( \frac{\sin i}{1.33} \right)$

Refractive Index

The refractive index ($n$) of a medium is a measure of how much light slows down when passing through it. It 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 vacuum is 1.00.

The refractive index of a substance is always greater than 1.00.

Examples and Calculations

Consider a ray of light traveling from air ($n_1 = 1.00$) into water ($n_2 = 1.33$). If the angle of incidence is 30 degrees, we can calculate the angle of refraction:

1. Using Snell's Law: $n_1 \sin i = n_2 \sin r$
2. Substituting the values: $1.00 \sin 30^\circ = 1.33 \sin r$
3. $\sin r = \frac{\sin 30^\circ}{1.33} = \frac{0.5}{1.33} \approx 0.3759$
4. $r = \sin^{-1}(0.3759) \approx 22.02^\circ$

Scenario	$n_1$ (Air)	$i$	$n_2$ (Water)	$r$
Air to Water	1.00	30°	1.33	22.02°
Water to Air	1.33	22.02°	1.00	30°

Note: The angle of incidence ($i$) is always greater than or equal to the angle of refraction ($r$) when light travels from a more dense medium to a less dense medium.