# Determining Wavelength of Laser Beam in Unknown Liquid

What is the wavelength of a helim-neon laser beam in an unknown liquid if it has a wavelength of 633 nm in air and takes 1.42 ns to travel through 26.0 cm of the liquid?

The wavelength of the laser beam in the unknown liquid is 474 nm. To determine this, we can use the formula v = λ * f, where v is the speed of light in a medium, λ is the wavelength of light in that medium, and f is the frequency of light. The speed of light in a vacuum is a constant, approximately 3.00 x 10^8 m/s. The wavelength of the laser beam in air is 633 nm (or 633 x 10^(-9) m) and the time it takes for the light to travel through 26.0 cm of the unknown liquid is 1.42 ns (or 1.42 x 10^(-9) s).

## Calculating Speed of Light in Unknown Liquid

**Speed of Light in Liquid:** v_liquid = distance / time

v_liquid = 0.26 m / (1.42 x 10^(-9) s) ≈ 183.099 x 10^6 m/s

## Finding Wavelength of Laser Beam in Liquid

**Formula:** λ_liquid = v_liquid / f

Since the frequency remains constant, we can use the speed of light in a vacuum:

λ_liquid = (3.00 x 10^8 m/s) / f

## Calculating Wavelength in Liquid

Substitute the wavelength in air and solve for the wavelength in the liquid:

λ_liquid = (3.00 x 10^8 m/s) / (633 x 10^(-9) m) ≈ 473.932 x 10^(-9) m ≈ 474 nm