In one section of the pool, there is a thin film of oil on the surface of the water. The thickness of the film is
1.0 X l0^-7 meter and the index of refraction of the oil is 1.5. The light source is now held in the air and illuminates the film at normal incidence, as shown above.
d. At which of the interfaces (air oil and oil water), if either, does the light undergo a 180° phase change upon reflection?
e. For what wavelengths in the visible spectrum will the intensity be a maximum in the reflected beam?
i need help on this plzzz
d. In order for light to undergo a 180° phase change upon reflection, there needs to be a change in refractive index. In this case, the light is traveling from air to oil, and then from oil to water.
When light travels from a medium with a lower refractive index (air) to a medium with a higher refractive index (oil), there is a phase change of 180° upon reflection. Therefore, at the air-oil interface, the light undergoes a 180° phase change upon reflection.
However, when light travels from a medium with a higher refractive index (oil) to a medium with a lower refractive index (water), there is no phase change upon reflection. Therefore, at the oil-water interface, the light does not undergo a 180° phase change upon reflection.
e. For thin film interference to occur, the thickness of the film (1.0 x 10^-7 meter) must be on the order of the wavelength of light. The path difference between the light reflected from the top surface and the bottom surface of the film must be an integer multiple of the wavelength of light for constructive interference to occur.
The condition for constructive interference in a thin film is given by the equation:
2nt = mλ
where:
- n is the refractive index of the film (in this case, oil)
- t is the thickness of the film
- m is an integer that represents the order of interference
- λ is the wavelength of light
To find the wavelengths for which the intensity is maximum in the reflected beam, we need to find the values of λ that satisfy the above equation. Since the order of interference can be any positive integer, we will consider m = 0, 1, 2, ...
For each value of m, we can rearrange the equation to solve for λ:
λ = (2nt) / m
Given that the refractive index of the oil is 1.5 and the thickness of the film is 1.0 x 10^-7 meter, we can calculate the values of λ for each value of m:
For m = 0: λ = (2 * 1.5 * 1.0 x 10^-7) / 0 = undefined (no solution)
For m = 1: λ = (2 * 1.5 * 1.0 x 10^-7) / 1 ≈ 3.0 x 10^-7 meter (wavelength in the visible spectrum)
For m = 2: λ = (2 * 1.5 * 1.0 x 10^-7) / 2 ≈ 1.5 x 10^-7 meter (wavelength in the visible spectrum)
For m = 3: λ = (2 * 1.5 * 1.0 x 10^-7) / 3 ≈ 1.0 x 10^-7 meter (wavelength in the visible spectrum)
...
Therefore, the wavelengths in the visible spectrum for which the intensity is a maximum in the reflected beam are approximately 3.0 x 10^-7 meter, 1.5 x 10^-7 meter, 1.0 x 10^-7 meter, etc.
To determine where the light undergoes a 180° phase change upon reflection and the wavelengths in the visible spectrum where the intensity is a maximum in the reflected beam, we need to consider the conditions for constructive interference and the phase changes that occur when light reflects off different interfaces.
First, let's start with the condition for constructive interference. Constructive interference occurs when the path difference between two interfering waves is a whole number multiple of the wavelength. This means that the waves will reinforce each other and result in a maximum intensity in the reflected beam.
Now, let's analyze the different interfaces:
1. Air-oil interface: When light reflects off the air-oil interface, there is a phase change of 180° due to the transition from a low refractive index (air) to a higher refractive index (oil). However, for constructive interference to occur, the path difference needs to be a whole number multiple of the wavelength. In this case, since the oil film thickness is very thin (1.0 x 10^-7 meter), the path difference is negligible compared to the wavelength of visible light. Therefore, there won't be any significant constructive interference at the air-oil interface.
2. Oil-water interface: Similarly, when light reflects off the oil-water interface, there is another phase change of 180° due to the transition from a high refractive index (oil) to a lower refractive index (water). Again, the oil film thickness (1.0 x 10^-7 meter) is much smaller than the wavelength of visible light, so the path difference is negligible. Therefore, there won't be any significant constructive interference at the oil-water interface either.
Considering the above analysis, the light does not undergo a 180° phase change upon reflection at either the air-oil or oil-water interface. Hence, constructive interference doesn't play a significant role in the reflected beam's intensity.
To find the wavelengths in the visible spectrum where the intensity is a maximum in the reflected beam, we need to consider the concept of thin film interference. Thin film interference occurs when the thickness of the film is on the order of the wavelength of light.
In this case, since the thickness of the oil film (1.0 x 10^-7 meter) is small compared to the wavelength of visible light (which ranges roughly from 400 to 700 nanometers), we can use the equation for thin film interference:
2t = mλ
where t is the thickness of the film, m is an integer representing the order of the interference, and λ is the wavelength of light.
For the reflected beam to have maximum intensity, we can focus on the first-order interference, where m = 1:
2t = λ
Solving for λ, we find that the wavelength for maximum intensity in the reflected beam will be twice the thickness of the oil film. However, since the question provided the thickness of the oil film (1.0 x 10^-7 meter), we can conclude that the maximum intensity will occur at a wavelength of 2 x (1.0 x 10^-7 meter).
Therefore, the maximum intensity in the reflected beam will occur at a wavelength of 2 x (1.0 x 10^-7 meter).