When light travels from one medium to another, such as from air to water or from air to glass, its wavelength can change. This phenomenon is known as refraction. To determine the new wavelength of light in the second medium, you can use the relationship between the speed, frequency, and wavelength of light.
The speed of light in a medium depends on the properties of that medium. It is generally lower in denser materials compared to less dense ones. The relationship between the speed of light (v), frequency (f), and wavelength (λ) is given by the equation:
v = f * λ
Where: v is the speed of light in the medium f is the frequency of the light λ is the wavelength of the light
When light passes from one medium to another, the frequency of the light remains constant. However, the speed of light changes, which leads to a change in the wavelength.
The relationship between the wavelengths in the two media can be expressed using Snell's law, which relates the angles of incidence and refraction and the indices of refraction for the two media:
n1 * sin(theta1) = n2 * sin(theta2)
Where: n1 and n2 are the indices of refraction of the initial and final media, respectively theta1 is the angle of incidence theta2 is the angle of refraction
Using Snell's law, you can derive the relationship between the wavelengths:
λ2 = (n1 / n2) * λ1
Where: λ1 is the wavelength of light in the initial medium λ2 is the wavelength of light in the final medium
So, to find the new wavelength of light in the second medium, you multiply the initial wavelength by the ratio of the indices of refraction of the two media.
It's important to note that the indices of refraction differ for different materials and for different wavelengths of light. Therefore, the change in wavelength will depend on the specific materials and the properties of the incident light.