A glass pane with index of refraction 1.5 is coated with a...

A glass pane with index of refraction 1.5 is coated with a thin film of a material with index of refraction 1.6 The coating is as thin as possible to produce maximum reflection for blue light. If this same material is used to coat a different kind of glass with index of refraction 1.9 the light reflected from the back surface of the film now experiences an inversion. Does the coating have to be thicker or thinner in this case to produce strong reflection? Explain.

Key Concepts

Thin Film Interference

Thin film interference results from the superposition of light waves reflected from the top and bottom boundaries of a thin film. The interference pattern is determined by the optical path difference between these reflected waves, which is influenced by the film’s thickness, the refractive indices of the involved media, and the wavelength of the incident light.

Phase Change upon Reflection

When light reflects from a boundary where the refractive index increases, it undergoes a half-wavelength phase shift (? radians). In contrast, if light reflects from a boundary where the refractive index decreases, no phase shift occurs. This phase change is crucial in thin film designs because it influences whether the reflected waves interfere constructively or destructively.

Optical Path Difference

The optical path difference is the additional distance, multiplied by the refractive index of the film, that one wave travels relative to another. In thin films, this extra distance is due to the round-trip travel of the light within the film, and adjusting the film’s thickness alters this path difference, which in turn affects the resultant phase difference between the interfering waves.

Constructive Interference Conditions

For constructive interference (leading to strong reflection), the reflected waves must be in phase. This may require a compensating phase shift from the film’s optical thickness. When the phase changes at the interfaces are known, the film thickness is chosen such that the accumulated phase difference from the path length complements these shifts, ensuring that the reflected waves add up constructively.

Transcript

Please give Ace some feedback