A The index of refraction for violet light in silica flint glass is 1.66 and that for red light

A The index of refraction for violet light in silica flint...

Key Concepts

Apex Angle

The apex angle of a prism is the angle between its two refracting surfaces. This angle plays an essential role in determining the overall deviation of light as it passes through the prism, influencing how the different colors spread out.

Index of Refraction

The index of refraction is a measure of how much light slows down when it enters a medium compared to its speed in a vacuum. It determines how light bends, or refracts, when passing from one medium to another according to the relative indices of refraction of the two media.

Dispersion

Dispersion is the phenomenon where different wavelengths (colors) of light travel at different speeds in a medium, resulting in different degrees of refraction. This effect causes the separation of white light into its constituent colors when it passes through materials like prisms.

Snell's Law

Snell's Law relates the angles of incidence and refraction to the indices of refraction of the two media in contact. It is fundamental in predicting how much a light ray will bend when it moves from one optical medium into another.

Prism

A prism is an optical element with flat, polished surfaces that refract light. When light enters and exits the prism, it is bent at each interface, and due to dispersion, different wavelengths emerge at different angles, producing a spectrum.

Angular Spread

Angular spread refers to the difference in deviation angles between different wavelengths of light emerging from a dispersive element like a prism. It quantifies the extent to which the visible spectrum is separated, providing a measure of the prism's dispersive power.

Transcript

00:01 So for this problem, we're told that we have a prism, and we have a ray of light entering that is comprised of white light, right? so there's a bunch of different colors in there.

00:18 And one of those colors, you know what, let's make this black, just to make it less confusing.

00:23 So one of these colors is red, and the other color is purple.

00:35 So they're both entering at the same time.

00:37 The purple gets deflected like this, and then it comes out like that.

00:42 And red gets deflected like that, and it comes out like that.

00:49 So we had to find this angular spread, right? i'm going to call this the change in theta.

00:58 So to find the answer to this problem, we're going to simplify the scenario, and just pretend that there's one light beam coming in for now, and it is exiting like this.

01:09 So there's a angle here that is theta 1 compared to the normal.

01:18 So there's that.

01:20 And then there is the theta 2.

01:24 Then we're going to talk about the theta 3, which is the angle of entry, the angle of exit, rather.

01:32 And then there's going to be a theta 4.

01:36 So we need to find the theta 4 for both of these light beams.

01:39 So how are we going to do that? we need to come up with a generalized equation.

01:42 For this.

01:43 So if we have our angle here, right, so let's start filling in the data.

01:49 So we have our apex angle of 60 degrees.

01:54 We have our theta 1 50 degrees.

01:58 We have our refractive index, and we'll call it n -red of 1 .62, and our n v violet of 1 .66.

02:14 So if we have have this theta 2 and this data 3 here, i'm going to have these angles called alpha and beta.

02:21 So we know that this angle, this angle and this angle all have to add up to 180.

02:26 So that's going to help us a lot.

02:28 Because if we know what theta 2 is, well, since this angle and this angle form 90 degrees, we can say that 90 minus theta 2 is equal to alpha.

02:41 So if that's the case, then 180 minus the apex angle, which is 60 minus beta is equal to, oh, hold on, minus alpha is equal to beta.

03:06 So that means that 120 minus 90 plus theta 2 is equal to beta, which means that 30 plus theta 2 is equal to beta.

03:22 And of course, beta plus theta3 is equal to 90, so 90 minus beta is equal to theta 3, which means that 60 minus theta 2 is equal to theta 3, which means that 60 minus theta 2 is equal to, theta 3 and again we're just rearranging all these equations.

03:46 So now that we know that we can start actually using some of the physics.

03:52 So that's just been geometry.

03:54 Now let's do some.

03:56 Let's do some physics if you'll give me a moment here.

04:04 So we're going to move this we're going to move this good lord up here so 60 is equal to you know what? this is hideous.

04:22 So we're going to erase that and we're going to erase that and don't want a soft eraser, you want a hard eraser.

04:29 We want that guy, and we want to get rid of you, say, 60 minus theta 2 is equal to theta 3...

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