Question

The equations for \(R\) and \(T\) in the \(E>U_{0}\) barrier are essentially the same as for light passing through a transparent film. It is possible to fabricate a thin film that reflects no light. Is it possible to fabricate one that transmits no light? Why or why not?

Short answer

No, it's not possible to fabricate a thin film that transmits no light. This is because complete absorption would result in an infinite heat build-up which is not physically possible, and 100% reflection is not allowed if reflectance is already zero.

Step-by-step solution

Understand Reflection and Transmission

Reflection and Transmission refer to the behavior of waves (in this case, light waves) as they encounter a medium (in this case, a thin film). Reflection refers to the wave bouncing off the medium, while Transmission refers to the wave passing through it. In our scenario, the amount of reflected and transmitted light depend on the film's properties such as its thickness and refractive index.

No Reflectance and Perfect Transmittance

A thin film which reflects no light means that the incident light wave is not reflected back, i.e., the reflectance is zero. This can be achieved by tuning the film's thickness and refractive index to cause destructive interference among the reflected light waves. Consequently, all light becomes transmitted light, making the transmittance equal to one (100% transmission). This is called anti-reflection coating, often used to minimize glare in optical devices like camera lenses, glasses, etc.

No Transmittance

In theory, a thin film transmitting no light implies that the film totally absorbs the incident light energy or reflects it all back such that nothing is transmitted. However, for the film to absorb all the incident light, it would effectively heat up infinitely, which is not physically possible. Therefore, a thin film that transmits no light (100% absorption or reflection) isn’t achievable.

Key concepts

Reflection and Transmission

Reflection and transmission are results of light interactions with materials. When light hits a surface, some of it bounces back. This is reflection. At the same time, some light passes through the material, which is transmission. Think of a glass window: you can see your reflection but also see through it. With thin films, reflection and transmission are vital concepts. When light strikes a film, parts reflect off of each layer. The amount that reflects or transmits depends heavily on several factors, like:

• The film's thickness
• The wavelength of incoming light
• The material's refractive index

Understanding these interactions allows us to design films that manipulate how much light reflects or transmits, used in applications like anti-glare coatings.

Refractive Index

The refractive index, typically denoted by the symbol \( n \), is a number that describes how light propagates through a medium. Different materials bend light in various ways. This bending occurs because the speed of light changes as it passes from one medium to another.

• For instance, light travels slower in water than in air, giving water a higher refractive index.
• This index helps determine how much light reflects or transmits through a material.

When designing thin films, choosing materials with the right refractive indices is crucial. By adjusting these properties, it's possible to control how waves interfere, ultimately dictating the reflection and transmission properties of the film.

Destructive Interference

Destructive interference occurs when two or more light waves align in such a way that they cancel each other out. In the case of thin films, by carefully choosing the film's thickness and its refractive index, the waves reflecting off the top and bottom surfaces interfere destructively.

• This results in no light being reflected, making the surface appear non-reflective.
• For lenses and optical devices, this is immensely useful as it reduces unwanted reflections that can obscure vision or imaging quality.

However, total blocking of transmission through destructive interference isn't feasible. This is because, for total non-transmission, the wave energy would need to be absorbed without any remainder, which isn't practically possible with thin films. The energy has to go somewhere, either transmitting or reflecting back, rather than being completely absorbed.