Calculating the Wavelength of a Laser Beam in an Unknown Liquid

Wavelength is the distance between two points of the two consecutive waves. In this scenario, the helium-neon laser beam has a wavelength in air of 633 nm.

The time taken by the laser beam to travel through 32.0 cm (0.32 m) of the unknown liquid is 1.38 ns (1.38 x 10^-9 s). To calculate the wavelength of the laser beam in the liquid, we first need to determine the speed of light in the liquid.

Calculating Speed of Light in the Unknown Liquid:

Speed of light = Distance / Time

Speed of light in the liquid = 0.32 m / 1.38 x 10^-9 s = 2.32 x 10^8 m/s

Determining Wavelength of the Laser Beam in the Liquid:

Frequency of light remains constant when it travels from one medium to another. Utilizing the formula:

V_air / λ_air = V_liquid / λ_liquid

Given values:

Speed of light in air (V_air) = 3 x 10^8 m/s

Wavelength of light in air (λ_air) = 633 nm

Speed of light in the liquid (V_liquid) = 2.32 x 10^8 m/s

Unknown wavelength in the liquid (λ_liquid) = ?

By substituting the above values into the formula and solving for the unknown wavelength in the liquid, we find:

λ_liquid = 489.52 nm

Therefore, the wavelength of the laser beam in the unknown liquid is 489.52 nm.