Calculate the frequency in hertz, wavelength in nm, and the velocity in m/s of light inside a material with a refractive index of 1.39. In vacuum, the light has a wavelength of 514.5nm
To calculate the frequency, wavelength, and velocity of light inside a material with a given refractive index, we can use the following formulas:
1. Frequency (f) = Speed of Light (c) / Wavelength (λ)
2. Wavelength inside material (λ_m) = Wavelength in vacuum (λ_v) / Refractive index (n)
3. Velocity inside material (v_m) = Speed of Light (c) / Refractive index (n)
Given:
Refractive index (n) = 1.39
Wavelength in vacuum (λ_v) = 514.5 nm
Step 1: Convert the wavelength in vacuum to meters
λ_v = 514.5 nm = 514.5 x 10^-9 m
Step 2: Calculate the wavelength inside the material using the formula:
λ_m = λ_v / n
λ_m = (514.5 x 10^-9 m) / 1.39
Step 3: Calculate the frequency using the formula:
f = c / λ_m, where c is the speed of light in a vacuum.
c = 3 x 10^8 m/s
f = (3 x 10^8 m/s) / λ_m
Step 4: Calculate the velocity inside the material using the formula:
v_m = c / n
v_m = (3 x 10^8 m/s) / 1.39
Now, let's calculate each of the values:
Step 1:
λ_v = 514.5 x 10^-9 m = 0.0005145 m
Step 2:
λ_m = (0.0005145 m) / 1.39
Step 3:
f = (3 x 10^8 m/s) / λ_m
Step 4:
v_m = (3 x 10^8 m/s) / 1.39
Calculating each of these values will give you the frequency in hertz, wavelength inside the material in nm, and velocity inside the material in m/s.