Calculating Wavelength of Laser Beam in Unknown Liquid

What is the wavelength of a helium-neon laser beam in an unknown liquid if it takes 1.28 ns to travel through 29.0 cm of the liquid?

Calculating Speed of Light in the Unknown Liquid

Using the formula speed = distance / time, we can determine the speed of light in the unknown liquid. The speed of light in a vacuum is approximately 3.00 x 10^8 m/s. Converting the distance of 29.0 cm to meters (0.29 m) and the time of 1.28 ns to seconds (1.28 x 10^-9 s), we get:
speed = 0.29 m / 1.28 x 10^-9 s = 226.56 x 10^6 m/s

Finding Refractive Index of the Unknown Liquid

Snell's Law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocity of light in the first medium to the velocity of light in the second medium. By applying Snell's Law, we can find the refractive index of the unknown liquid:
n = speed of light in air / speed of light in the liquid
Calculating: n = 3.00 x 10^8 m/s / 226.56 x 10^6 m/s = 1.324

Determining Wavelength of Laser Beam in the Unknown Liquid

To find the wavelength of the laser beam in the unknown liquid, we use the formula: wavelength in liquid = wavelength in air / refractive index of the liquid
Plugging in the values: wavelength in liquid = 633 nm / 1.324 = 478.9 nm Therefore, the wavelength of the helium-neon laser beam in the unknown liquid is 478.9 nm.

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