When you look through a 3.7 mm thick window comprised of a material whose refractive index is 1.59, by what time interval is the light you see delayed by having to go through glass instead of air?
By how many wavelengths is it delayed, if its vacuum wavelength is 600 nm?
To find the time interval by which light is delayed when passing through a material, we can use the formula:
Δt = t2 - t1
Where:
Δt is the time interval of delay
t2 is the time taken by light to pass through the material
t1 is the time taken by light to pass through air
The time taken by light to pass through a medium can be calculated using the equation:
t = d / c
Where:
t is the time taken by light
d is the thickness of the material
c is the speed of light in the material
First, let's calculate t2, the time taken by light to pass through the 3.7 mm thick window.
Since the refractive index (n) of the material is given as 1.59, we can use the following equation to calculate the speed of light in the material (v):
v = c / n
Where:
c is the speed of light in a vacuum (approximately 3 x 10^8 m/s)
Substituting the values, we get:
v = (3 x 10^8 m/s) / 1.59
Now, we can calculate t2 using the formula:
t2 = d / v
Substituting the values, we have:
t2 = (3.7 x 10^-3 m) / v
Next, let's calculate t1, the time taken by light to pass through air. Since the speed of light in air is very close to the speed of light in a vacuum, we can approximate it as:
c_air ≈ c
Using the same formula to calculate t1:
t1 = d / c_air
Substituting the values, we have:
t1 = (3.7 x 10^-3 m) / c
Now, let's calculate the time interval of delay (Δt):
Δt = t2 - t1
With the calculated values of t2 and t1, plug them into the equation to find Δt.
To calculate the number of wavelengths by which the light is delayed, we can use the formula:
Δλ = Δt / t_wave
Where:
Δλ is the number of wavelengths delayed
Δt is the time delay
t_wave is the time taken for one wavelength
Given that the vacuum wavelength (λ_wave) is 600 nm (600 x 10^-9 m), we can calculate t_wave using the formula:
t_wave = λ_wave / c
Substituting the values, we have:
t_wave = (600 x 10^-9 m) / c
Finally, we can calculate Δλ by substituting the values of Δt and t_wave into the formula:
Δλ = Δt / t_wave
In this case, the time delay (Δt) is the value calculated earlier, and t_wave is the value calculated just now.
By following these steps, you should be able to calculate the time interval and the number of wavelengths by which the light is delayed when passing through the glass window.