Angular Wavenumber of Helium-Neon Laser Light in Water

What is the numerical value of the angular wavenumber of helium-neon laser light in water?

Calculate the angular wavenumber of neon laser light having a wavelength of 633 nm in water (n=1.33).

Numerical Value of Angular Wavenumber of Helium-Neon Laser Light in Water

The angular wavenumber k of neon laser light with a wavelength of 633 nm in water is 1.32 x 10⁷ m⁻¹.

When considering the angular wavenumber of helium-neon laser light in water, it is essential to take into account the refractive index of water (n=1.33). This value affects the wavelength of the light when it passes through water.

To find the angular wavenumber k of the radiation in water, we follow these steps:

1. Convert the wavelength from nanometers (nm) to meters (m):

λ (in meters) = 633 nm * (1 meter / 1,000,000,000 nm) = 6.33 x 10⁻⁷ m

2. Find the wavelength in water by dividing the vacuum wavelength by the refractive index (n) of water:

λ_water = λ_vacuum / n = (6.33 x 10⁻⁷ m) / 1.33 = 4.76 x 10⁻⁷ m

3. Calculate the angular wavenumber k using the formula: k = 2π / λ_water

k = 2π / (4.76 x 10⁻⁷ m) = 1.32 x 10⁷ m⁻¹

Therefore, the numerical value of the angular wavenumber k of helium-neon laser light in water is 1.32 x 10⁷ m⁻¹.