Question

Explain how you can work out the

relationship between the frequency of a
ray of light and its angle of refracton.

Answer 1

The speed of light changes as it moves between media. This causes refraction. Angles of refraction can be calculated using known speeds or wavelengths. Beyond the critical angle, light is reflected.

Answer 2

As the frequency of light increases, the refractive index of the prism increases, resulting in a larger angle of refraction for higher-frequency colors (e.g., violet) compared to lower-frequency colors (e.g., red) when passing through a prism.

The relationship between the frequency of a ray of light and its angle of refraction can be understood through the phenomenon of dispersion, which occurs when light passes through a prism. Dispersion is the splitting of light into its constituent colors due to differences in the refractive indices of different colors of light.

When white light passes through a prism, it undergoes refraction, and each color (wavelength) is bent by a slightly different amount. This bending is a result of the varying refractive indices for different colors in the prism material. The shorter wavelengths, associated with higher frequencies (such as violet light), are bent more than the longer wavelengths (associated with lower frequencies, such as red light).

The relationship between the frequency (f) and the angle of refraction (
`\theta\)`) can be expressed using Snell's Law:

`\[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \]`

where:

-
`\(n_1\) and \(n_2\)` are the refractive indices of the two media (air and the prism),

-
`\(\theta_1\) and \(\theta_2\)` are the angles of incidence and refraction, respectively.

Since the refractive index (n) is related to the speed of light in a medium (v) by n = c/v, where c is the speed of light in a vacuum, and v is the speed of light in the medium, the frequency (f) can be related to the refractive index. The higher the frequency, the greater the refractive index and the greater the angle of refraction.