Problem 17.6
A helium-neon laser beam has a wavelength in air of 633nm . It takes 1.48 ns for the light to travel through 31.0 cm of an unknown liquid.
Part A -
What is the wavelength of the laser beam in the liquid?
Express your answer with the appropriate units.
speed= distance/time=.31m/1.48E-9sec
wavelength is prop to speed.
wavelength=633nm*speedabove/speedinair
To find the wavelength of the laser beam in the liquid, we can use the formula:
λ(liquid) = λ(air) / n(liquid)
where λ(liquid) represents the wavelength of light in the liquid, λ(air) represents the wavelength of light in air, and n(liquid) represents the refractive index of the liquid.
First, we need to calculate the refractive index of the liquid using the given information.
Given:
λ(air) = 633 nm (nanometers)
t = 1.48 ns (nanoseconds)
d = 31.0 cm (centimeters)
We can find the refractive index of the liquid using the formula:
n(liquid) = c * t / d
where c is the speed of light in vacuum.
The speed of light in vacuum is approximately 3.00 x 10^8 m/s (meters per second).
Converting the given quantities to the appropriate units:
λ(air) = 633 nm = 633 x 10^(-9) m
t = 1.48 ns = 1.48 x 10^(-9) s
d = 31.0 cm = 31.0 x 10^(-2) m
Substituting the values into the formula:
n(liquid) = (3.00 x 10^8 m/s) * (1.48 x 10^(-9) s) / (31.0 x 10^(-2) m)
Calculating the refractive index:
n(liquid) = 4.320 x 10^(-4)
Now that we have the refractive index of the liquid, we can find the wavelength of the laser beam in the liquid using the first formula:
λ(liquid) = λ(air) / n(liquid)
Substituting the values:
λ(liquid) = (633 x 10^(-9) m) / (4.320 x 10^(-4))
Calculating the wavelength in the liquid:
λ(liquid) = 1.47 x 10^(-6) m
Therefore, the wavelength of the laser beam in the liquid is approximately 1.47 μm (micrometers).