A helium-neon laser beam has a wavelength in air of 633 nm. It takes 1.48 ns for the light to travel through 34.0 cm of an unknown liquid.
What is the wavelength of the laser beam in the liquid? (answer in ns)
To find the wavelength of the laser beam in the liquid, we can use the equation:
wavelength in liquid = wavelength in air / refractive index of the liquid
The refractive index of a substance is a measure of how light propagates through it. It tells us how much the speed of light changes in that medium. Since we have the time it takes for light to travel through the liquid, we can calculate the refractive index using the equation:
refractive index of the liquid = speed of light in vacuum / speed of light in the liquid
The speed of light in a vacuum is a well-known constant: 2.998 x 10^8 meters per second. We just need to convert the distance traveled by light through the liquid to meters and divide it by the time it took.
So, let's calculate it step by step:
Step 1: Convert the distance from centimeters to meters:
34.0 cm = 0.34 meters
Step 2: Calculate the speed of light in the liquid:
speed of light in liquid = distance / time = 0.34 meters / 1.48 ns
To keep the units consistent, we need to convert nanoseconds to seconds:
1 ns = 1 x 10^-9 s
So, the speed of light in the liquid is:
speed of light in liquid = 0.34 meters / (1.48 x 10^-9 s) = 2.297 x 10^8 meters per second
Step 3: Calculate the refractive index of the liquid:
refractive index of the liquid = speed of light in vacuum / speed of light in the liquid
refractive index of the liquid = (2.998 x 10^8 meters per second) / (2.297 x 10^8 meters per second)
Step 4: Finally, calculate the wavelength in the liquid:
wavelength in liquid = wavelength in air / refractive index of the liquid
wavelength in liquid = 633 nm / refractive index of the liquid
Substituting the values, we get:
wavelength in liquid = 633 nm / (refractive index of the liquid calculated in step 3)
By calculating these steps, we can find the wavelength of the laser beam in the liquid.