We wish to coat flat glass (n= 1.50) with a transparent material (n=1.25) so that reflection of

We wish to coat flat glass (n= 1.50) with a transparent...

Key Concepts

Optical Path Difference

The optical path difference is the product of the physical path length that light travels in a medium and the medium’s refractive index. This concept is essential in thin film interference because it determines the phase difference between light waves that traverse different paths, thereby affecting the interference outcome.

Quarter-Wave Coating

A quarter-wave coating is a design strategy for anti-reflection films where the thickness of the coating is such that the optical thickness is one-quarter of the target wavelength. This choice causes the light reflected from the top interface to be out of phase with that reflected from the bottom interface by ?, leading to destructive interference and reduced reflection.

Phase Shifts upon Reflection

Light can experience a phase shift when reflecting at the interface between two media with different refractive indices. Typically, a phase shift of ? (or half a wavelength) occurs when light reflects from a medium of lower refractive index to one with a higher refractive index, which is crucial for determining the conditions for constructive or destructive interference in thin films.

Thin Film Interference

Thin film interference is a phenomenon that occurs when light waves reflect off the different boundaries of a thin layer and subsequently interfere with each other. The interference can be constructive or destructive depending on the phase difference between the reflections. This concept is central in applications like anti-reflection coatings where controlling the interference minimizes unwanted reflections.

Transcript

00:01 In this problem, we have a glass surface coated with some material, and this coating has some thickness d.

00:12 We're told it has an index of a fraction of 1 .25.

00:16 The material the coating is made of has an index of a fraction of 1 .25, and i'm going to call that n1.

00:23 And then we're told that the glass has an index of a fraction n2 of 1 .5.

00:30 So what's going to happen is light's going to come in from air here, left to right, and air has a index of a fraction i'll call n -not of 1 and part of it's going to be reflected off of this first surface and part of it's going to be transmitted and then reflected off of the second surface we'll draw that in red so that in total we have two reflected rays and these rays are going to be in general they're going to end up phase shifted and what the problem is asking is what does this thickness d have to be such that these two red and black reflected waves come out 180 degrees out of phase.

01:15 So the black ray might be like this, and the red ray will be exactly 180 degrees out of phase.

01:30 So that the net wave is zero, or has zero amplitude.

01:36 So that means that the extra path that's traveled by the initially transmitted ray has to be some half multiple of the wavelength.

01:47 And so what's the extra path traveled? well, it's once to the right and once to the left.

01:52 So that's two times this thickness d.

01:55 So we have 2d must equal some half multiple of the wavelength.

02:02 So we can write that as lambda times and then n plus one half, where n is an integer...

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