How to Determine the Wavelength of a Helium-Neon Laser Beam in an Unknown Liquid
What is the wavelength of the helium-neon laser beam in the unknown liquid?
n₁λ₁ = n₂λ₂
where n₁ and n₂ are the refractive indices of the initial and final mediums, and λ₁ and λ₂ are the corresponding wavelengths.
In this case, the helium-neon laser beam travels from air (the initial medium) to the unknown liquid (the final medium). The wavelength of the laser beam in air is given as 633 nm.
We also know that the time it takes for the laser beam to travel through a distance in the liquid is 1.48 ns, and the distance is 34.0 cm.
Calculating the Refractive Index of the Liquid:
speed in the liquid (c₂) = distance in the liquid (d) / time (t)
Next, we can calculate the refractive index of the liquid (n₂) using the speed of light in air (c₁) and the speed of light in the liquid (c₂):
n₂ = c₁ / c₂
Finally, we can rearrange the formula n₁λ₁ = n₂λ₂ to solve for the wavelength of the laser beam in the liquid (λ₂). By substituting the known values, we can calculate λ₂.
By following these steps, we can determine that the wavelength of the helium-neon laser beam in the unknown liquid is shorter than 633 nm.