Resources | Subject Notes | Physics
This section explores the bending of light as it passes from one transparent medium to another. We will define the refractive index and understand how it relates to the speed of light in different media.
The refractive index, denoted by n, is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in a particular medium (v). It is a dimensionless number greater than or equal to 1.
Mathematically, this is expressed as:
$$n = \frac{c}{v}$$
Where:
The refractive index of a vacuum is defined as 1, as it represents the maximum possible speed of light.
Refraction occurs because light travels at different speeds in different media. When light moves from a medium with one refractive index to a medium with a different refractive index, its speed changes, causing it to bend.
The amount of bending depends on the difference in refractive indices between the two media. A larger difference results in more bending.
The refractive index of a medium is related to the speed of light in that medium. Generally, the higher the refractive index, the slower the speed of light in that medium.
A table summarizing the refractive indices of some common media is shown below:
| Medium | Refractive Index (n) |
|---|---|
| Vacuum | 1.00 |
| Air | 1.00 |
| Water | 1.33 |
| Glass | 1.50 - 1.90 (depending on the type of glass) |
| Diamond | 2.42 |
Snell's Law describes the relationship between the angles of incidence and refraction. It states that:
$$n_1 \sin{\theta_1} = n_2 \sin{\theta_2}$$
Where:
Snell's Law is a fundamental principle in understanding refraction and is used to calculate the angle of refraction given the angle of incidence and the refractive indices of the two media.
Total internal reflection occurs when light travels from a medium with a higher refractive index to a medium with a lower refractive index, and the angle of incidence is greater than the critical angle.
The critical angle (θc) is the angle of incidence at which the angle of refraction is 90 degrees.
The critical angle can be calculated using the following formula:
$$ \sin{\theta_c} = \frac{n_2}{n_1} $$
Where:
If the angle of incidence is greater than the critical angle, all the light is reflected back into the original medium, a phenomenon known as total internal reflection. This is the principle behind optical fibers.