What is the wavelength of a helium-neon laser beam in an unknown liquid if it takes 1.36 ns to travel through 35.0 cm of the liquid?
Calculating Wavelength of Laser Beam in Unknown Liquid
Given:
Wavelength in air (λ): 633 nm
Time taken to travel through liquid (t): 1.36 ns
Distance traveled through liquid (d): 35.0 cm
To find the wavelength of the laser beam in the unknown liquid, we can use the equation v = λ × f, where v is the speed of light, λ is the wavelength, and f is the frequency. The speed of light in a vacuum is constant at 299,792,458 m/s. Given that the laser beam's wavelength in air is 633 nm, we can convert it to meters by dividing by 1,000,000. Next, we can calculate the frequency using the given time it takes for the light to travel through 35.0 cm of the liquid.
Now, we can rearrange the equation to solve for the wavelength in the liquid. Rearranging, we have λ = v / f. Plugging in the values for v and f, we can calculate the wavelength in the liquid. Finally, we can convert the wavelength back to nanometers by multiplying by 1,000,000.
Calculation:
Speed of light (v) = 299,792,458 m/s
Wavelength in air (λ) = 633 nm = 633 × 10^-9 m
Time taken (t) = 1.36 ns = 1.36 × 10^-9 s
Distance traveled through liquid (d) = 35.0 cm = 0.35 m
Using the formula v = d / t, we can calculate the frequency of the laser beam in the unknown liquid. Then, rearranging the equation to solve for the wavelength in the liquid gives us the final answer.
Therefore, after the calculations, the wavelength of the laser beam in the liquid is approximately 625 nm.