Calculating Wavelength of Laser Beam in Unknown Liquid

Explanation:

Calculating Speed of Light in the Liquid: The speed of light in the liquid can be calculated using the formula v = d/t, where d is the distance traveled (30.0 cm) and t is the time taken (1.38 ns). Converting the units to meters and seconds, we get v ≈ 2.17 x 10^8 m/s.

Calculating Refractive Index of the Liquid: The refractive index of the liquid can be found using the formula n = c/v, where c is the speed of light in vacuum (approximately 3.00 x 10^8 m/s) and v is the speed of light in the liquid. Plugging in the values, we get n ≈ 3.00 x 10^8 m/s / 2.17 x 10^8 m/s ≈ 1.38.

Calculating Wavelength in the Liquid: Finally, the wavelength of the laser beam in the liquid can be determined using the formula λ = λ_o/n. Plugging in the values, we get λ ≈ 633 nm / 1.38 ≈ 459 nm. Therefore, the wavelength of the laser beam in the unknown liquid is approximately 459 nm.