A beam of light in air is incident upon a stack of four fla...

A beam of light in air is incident upon a stack of four fla transparent materials with indices of refraction $1.20,1.40$, 1.32, and $1.28$. If the angle of incidence for the beam on the first of the four materials is $60.0^{\circ}$, what angle does the beam make with the normal when it emerges into the ain after passing through the entire stack?

Key Concepts

Index of Refraction

This concept represents how much a ray of light slows down when it enters a medium from a vacuum or another medium. The ratio of the speed of light in vacuum to its speed in the medium defines the refractive index, which in turn influences the bending of the light as dictated by Snell’s Law.

Angle of Incidence

This term describes the angle between an incoming ray of light and the normal to the interface at the point of contact. It is critical for applying Snell’s Law correctly and determines how the light will refract when entering another medium.

Snell’s Law

This is the fundamental principle that governs the change in the direction of light when it passes from one medium to another. It states that the product of the refractive index and the sine of the angle of incidence is constant across the interface, which allows one to determine the angle of refraction in each subsequent medium.

Refraction at Multiple Interfaces

When light passes through several layers with different refractive indices, Snell’s Law is applied at each boundary. The cumulative effect of these refractions determines the final direction of the light as it emerges from the layered system into the original or a different medium.

Transcript

00:01 In this problem, we are going to follow a ray of light through four flat pieces of some sort of transparent material, each piece having its own thickness and its own index of refraction.

00:16 What we'll be needing to use is snells law, which governs the angle that a ray of light makes to the normal on one side of a material to the other.

00:31 So on one side you have the index of refraction a times the sign of the angle a is equal to the same product on the opposite side.

00:45 And it's important to note that those angles must be measured with respect to the normal.

00:51 Now, one thing that is true about a flat piece is that the ray will exit, the material at the same angle it went in, but slightly displaced.

01:16 And this is important that the normals to the surface do not point in different directions.

01:23 That is the whole deal with a flat piece.

01:26 The ray will exit the material at the same angle as it came in.

01:35 And what this means, so i'll draw like a little flat piece over here.

01:40 It's not perfectly flat, but we'll get the idea.

01:48 So the ray, let's pretend that the n is bigger than it is outside, so we can draw what this ray will do with respect to the normal.

02:04 In this case, it will bend towards the normal.

02:08 When it gets to the other side, it will bend exactly back the way it came in away from the normal.

02:22 But it is important that the two normals, the things that are perpendicular to the surface, normals point the same direction on entry and exit.

02:43 Okay, so what this means is that even if you have a large stack of four plates, the angle should.

02:53 Now, it'll be displaced, but it should do some interesting things to the material, but it will bend back to the 16...

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