Thinnest film in which the reflected light will be a maximum?

In summary, the conversation is about finding the thinnest film in which reflected light will be at its maximum when monochromatic light strikes it at normal incidence. The two formulas discussed are 2d = (m+1/2)(lambda/nfilm) and 2d = m(lambda/nfilm), with the latter being used to solve for d. There is some disagreement between the speaker and someone else in their class about the correct answer, with one saying d = lambda/2n and the other saying d = lambda/4n. A reference is provided for further insight.
  • #1
vrobins1
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Homework Statement



Monochromatic light, at normal incidence, strikes a thin film in air. If (lambda) denotes the wavelength in the film, what is the thinnest film in which he reflected light will be a maximum?

Homework Equations



2d = (m+1/2)(lambda/nfilm) for minimal reflection and

2d = m(lambda/nfilm) for max reflection

The Attempt at a Solution



I used the second formula above:

2d = m(lambda/n) and solved for d;
I got d = lambda/2n , but someone else in my class says it is lamba/4n,

Can anyone offer any insight? Thanks!
 
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  • #3


I can provide some clarification on this topic. The thinnest film in which the reflected light will be a maximum depends on the specific conditions and properties of the film and the incident light. The equations you have provided are correct in general, but they may not necessarily give the exact answer in every case.

To determine the thinnest film for maximum reflection, we need to consider the phase difference between the incident and reflected light waves. This phase difference is determined by the thickness of the film, the refractive index of the film, and the wavelength of the incident light. The equations you have provided give the conditions for minimal and maximum reflection, but they do not take into account the phase difference.

In order to find the thinnest film for maximum reflection, we need to use the condition for constructive interference, which is when the phase difference between the incident and reflected waves is an integer multiple of 2π. This can be expressed as:

2d = m(lambda/nfilm) + (2π)

Where m is an integer representing the number of complete cycles of the wave, lambda is the wavelength in the film, and nfilm is the refractive index of the film.

Solving for d, we get:

d = (m(lambda/nfilm) + (2π))/2

Now, since we want to find the thinnest film, we want to minimize the value of d. This occurs when m = 0, as any other integer value would result in a larger value for d. Therefore, the thinnest film for maximum reflection would be:

d = (2π)/2 = π

This means that the thinnest film for maximum reflection would have a thickness of half the wavelength of the incident light in the film.

I hope this helps to clarify the concept. Keep in mind that in some cases, the thinnest film for maximum reflection may not be exactly half the wavelength, as other factors such as the angle of incidence and the polarization of the light may also play a role. It is important to consider all these factors in order to accurately determine the thinnest film for maximum reflection in a given scenario.
 

1. What is the thinnest film in which the reflected light will be a maximum?

The thinnest film in which the reflected light will be a maximum is called a Fabry-Perot interferometer. It is a type of optical interferometer that consists of two partially reflecting mirrors separated by a small distance.

2. How does the thickness of the film affect the maximum reflected light?

The thickness of the film plays a crucial role in determining the maximum reflected light. As the thickness of the film decreases, the maximum reflected light increases. However, if the film becomes too thin, the maximum reflected light will decrease due to interference effects.

3. What is the relationship between the refractive index of the film and the maximum reflected light?

The refractive index of the film also affects the maximum reflected light. The higher the refractive index, the thinner the film needs to be in order to achieve the maximum reflected light. This is because a higher refractive index causes a larger phase shift in the reflected light, resulting in constructive interference.

4. How does the angle of incidence affect the maximum reflected light in a thin film?

The angle of incidence also plays a role in the maximum reflected light in a thin film. At certain angles of incidence, the reflected light will be completely extinguished due to destructive interference. However, at other angles of incidence, the reflected light will be maximized due to constructive interference.

5. Can the thinnest film in which the reflected light will be a maximum be used in practical applications?

Yes, the Fabry-Perot interferometer, which is the thinnest film in which the reflected light will be a maximum, has many practical applications. It is used in laser cavities, spectroscopy, and as a tunable filter. It also plays a crucial role in the operation of fiber-optic communication systems.

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